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  Subjects -> MATHEMATICS (Total: 955 journals)
    - APPLIED MATHEMATICS (82 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (706 journals)
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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Finite Fields and Their Applications
  [SJR: 1.096]   [H-I: 29]   [3 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 1071-5797 - ISSN (Online) 1090-2465
   Published by Elsevier Homepage  [3175 journals]
  • Permutation polynomials, fractional polynomials, and algebraic curves
    • Authors: Daniele Bartoli; Massimo Giulietti
      Pages: 1 - 16
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Daniele Bartoli, Massimo Giulietti
      In this note we prove a conjecture by Li, Qu, Li, and Fu on permutation trinomials over F 3 2 k . In addition, new examples and generalizations of some families of permutation polynomials of F 3 k and F 5 k are given. We also study permutation quadrinomials of type A x q ( q − 1 ) + 1 + B x 2 ( q − 1 ) + 1 + C x q + x . Our method is based on the investigation of an algebraic curve associated with a fractional polynomial over a finite field.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.001
      Issue No: Vol. 51 (2018)
       
  • Self-dual codes with an automorphism of order 7 and s-extremal codes of
           length 68
    • Authors: Nikolay Yankov; Milena Ivanova; Moon Ho Lee
      Pages: 17 - 30
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Nikolay Yankov, Milena Ivanova, Moon Ho Lee
      This paper studies and classifies optimal binary self-dual codes having an automorphism of order 7 with 9 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order p. There are exactly 69781 inequivalent binary self-dual [ 64 , 32 , 12 ] codes with an automorphism of type 7 − ( 9 , 1 ) . As for binary [ 66 , 33 , 12 ] self-dual codes with an automorphism of type 7 − ( 9 , 3 ) there are 1652432 such codes. We also construct more than 4 million new optimal codes of length 68 among which are the first known examples of the very elusive s-extremal self-dual codes. We prove the nonexistence of [ 70 , 35 , 14 ] codes with an automorphism of type 7 − ( 9 , 7 ) . Most of the constructed codes for all lengths have weight enumerators for which the existence was not known before.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2017.12.001
      Issue No: Vol. 51 (2018)
       
  • Permutation polynomials (xpm−x+δ)s1+(xpm−x+δ)s2+x
           over Fpn
    • Authors: Lisha Li; Shi Wang; Chaoyun Li; Xiangyong Zeng
      Pages: 31 - 61
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Lisha Li, Shi Wang, Chaoyun Li, Xiangyong Zeng
      In this paper, we propose several classes of permutation polynomials with the form ( x p m − x + δ ) s 1 + ( x p m − x + δ ) s 2 + x over finite fields. The permutation behavior of the proposed polynomials is investigated by the AGW criterion and determination of the number of solutions to certain equations over finite fields.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.003
      Issue No: Vol. 51 (2018)
       
  • Idempotents and codes in some non semi-simple metacyclic group algebras
    • Authors: Mostafa Alaoui Abdallaoui; Mohammed El Badry; Abdelfattah Haily
      Pages: 62 - 70
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Mostafa Alaoui Abdallaoui, Mohammed El Badry, Abdelfattah Haily
      We consider group algebra of a metacyclic group of order p n q over a field of characteristic p, where p and q are distinct prime numbers. We determine the terms of the primary decomposition of this algebra. The central primitive idempotents are also calculated. In the end we give the characteristics (dimension and minimal weight) of codes generated by these idempotents.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.004
      Issue No: Vol. 51 (2018)
       
  • Constructions for self-dual codes induced from group rings
    • Authors: Joe Gildea; Abidin Kaya; Rhian Taylor; Bahattin Yildiz
      Pages: 71 - 92
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Joe Gildea, Abidin Kaya, Rhian Taylor, Bahattin Yildiz
      In this work, we establish a strong connection between group rings and self-dual codes. We prove that a group ring element corresponds to a self-dual code if and only if it is a unitary unit. We also show that the double-circulant and four-circulant constructions come from cyclic and dihedral groups, respectively. Using groups of order 8 and 16 we find many new construction methods, in addition to the well-known methods, for self-dual codes. We establish the relevance of these new constructions by finding many extremal binary self-dual codes using them, which we list in several tables. In particular, we construct 10 new extremal binary self-dual codes of length 68.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.002
      Issue No: Vol. 51 (2018)
       
  • Trace of products in finite fields
    • Authors: Cathy Swaenepoel
      Pages: 93 - 129
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Cathy Swaenepoel
      Let p be a prime number and let q = p r . If C and D are large subsets of F q ⁎ we study the trace of products cd with c ∈ C and d ∈ D and show that it is well distributed in F p . We give an optimal condition (up to an absolute constant factor) on the size of the subsets C and D to ensure that the trace of products cd takes any given value in F p . We also give a condition (optimal up to an absolute constant factor in most cases) on the size of the subsets C and D to ensure that the trace of cd meets the set of k-th powers for k ≥ 1 , respectively the set of generators. Our method will enable us to take sets C and D whose size is substantially below q . Character sums and Gaussian sums over F p and F q will play an important role in the proofs. Some estimates lead to interesting combinatorial questions in finite fields.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.005
      Issue No: Vol. 51 (2018)
       
  • Generalized Hamming weights of affine Cartesian codes
    • Authors: Peter Beelen; Mrinmoy Datta
      Pages: 130 - 145
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Peter Beelen, Mrinmoy Datta
      Let F be any field and A 1 , … , A m be finite subsets of F . We determine the maximum number of common zeroes a linearly independent family of r polynomials of degree at most d of F [ x 1 , … , x m ] can have in A 1 × … × A m . In the case when F is a finite field, our results resolve the problem of determining the generalized Hamming weights of affine Cartesian codes. This is a generalization of the work of Heijnen and Pellikaan where these were determined for the generalized Reed–Muller codes. Finally, we determine the duals of affine Cartesian codes and compute their generalized Hamming weights as well.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.006
      Issue No: Vol. 51 (2018)
       
  • A minimum distance bound for 2-dimension λ-quasi-twisted codes over
           finite fields
    • Authors: Jingjie Lv; Jian Gao
      Pages: 146 - 167
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Jingjie Lv, Jian Gao
      We provide a concatenated structure for 2-dimension λ-quasi-twisted (λ-Q2DT) codes over F q , which is a generalization of the concatenated structure for 2-dimension quasi-cyclic (Q2DC) codes. Further, by trace representations of λ-constacyclic codes, λ-quasi-twisted codes, 2-dimension λ-constacyclic codes and λ-Q2DT codes, we obtain a general lower bound of the minimum distance for λ-Q2DT codes of length mℓk, where m , ℓ and k are relatively prime to q.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.008
      Issue No: Vol. 51 (2018)
       
  • On Kassel–Reutenauer q-analog of the sum of divisors and the ring
           F3[X]/X2F3[X]
    • Authors: José Manuel Rodríguez Caballero
      Pages: 183 - 190
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): José Manuel Rodríguez Caballero
      A q-analog P n ( q ) of the sum of divisors of n was introduced by C. Kassel and C. Reutenauer in a combinatorial setting and by T. Hausel, E. Letellier, F. Rodriguez-Villegas in a Hodge-theoretic setting. We study the reduction modulo 3 of the polynomial P n ( q ) with respect to the ideal ( q 2 + q + 1 ) F 3 [ q ] .

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.010
      Issue No: Vol. 51 (2018)
       
  • On common zeros of a pair of quadratic forms over a finite field
    • Authors: A.S. Sivatski
      Pages: 191 - 203
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): A.S. Sivatski
      Let F be a finite field of characteristic distinct from 2, f and g quadratic forms over F, dim ⁡ f = dim ⁡ g = n . A particular case of Chevalley's theorem claims that if n ≥ 5 , then f and g have a common zero. We give an algorithm, which establishes whether f and g have a common zero in the case n ≤ 4 . The most interesting case is n = 4 . In particular, we show that if n = 4 and det ⁡ ( f + t g ) is a squarefree polynomial of degree different from 2, then f and g have a common zero. We investigate the orbits of pairs of 4-dimensional forms ( f , g ) under the action of the group GL 4 ( F ) , provided f and g do not have a common zero. In particular, it turns out that for any polynomial p ( t ) of degree at most 4 up to the above action there exist at most two pairs ( f , g ) such that det ⁡ ( f + t g ) = p ( t ) , and the forms f, g do not have a common zero. The proofs heavily use Brumer's theorem and the Hasse–Minkowski theorem.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.007
      Issue No: Vol. 51 (2018)
       
  • The k-subset sum problem over finite fields
    • Authors: Weiqiong Wang; Jennifer Nguyen
      Pages: 204 - 217
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Weiqiong Wang, Jennifer Nguyen
      The subset sum problem is an important theoretical problem with many applications, such as in coding theory, cryptography, graph theory and other fields. One of the many aspects of this problem is to answer the solvability of the k-subset sum problem. It has been proven to be NP-hard in general. However, if the evaluation set has some special algebraic structure, it is possible to obtain some good conclusions. Zhu, Wan and Keti proposed partial results of this problem over two special kinds of evaluation sets. We generalize their conclusions in this paper, and propose asymptotical results of the solvability of the k-subset sum problem by using estimates of additive character sums over the evaluation set, together with the Brun sieve and the new sieve proposed by Li and Wan. We also apply the former two examples as application of our results.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.02.001
      Issue No: Vol. 51 (2018)
       
  • A group action on multivariate polynomials over finite fields
    • Authors: Lucas Reis
      Pages: 218 - 237
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Lucas Reis
      Let F q be the finite field with q elements, where q is a power of a prime p. Recently, a particular action of the group GL 2 ( F q ) on irreducible polynomials in F q [ x ] has been introduced and many questions concerning the invariant polynomials have been discussed. In this paper, we give a natural extension of this action on the polynomial ring F q [ x 1 , … , x n ] and study the algebraic properties of the invariant elements.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.011
      Issue No: Vol. 51 (2018)
       
  • Multi-twisted codes over finite fields and their dual codes
    • Authors: Anuradha Sharma; Varsha Chauhan; Harshdeep Singh
      Pages: 270 - 297
      Abstract: Publication date: May 2018
      Source:Finite Fields and Their Applications, Volume 51
      Author(s): Anuradha Sharma, Varsha Chauhan, Harshdeep Singh
      Let F q denote the finite field of order q, let m 1 , m 2 , ⋯ , m ℓ be positive integers satisfying gcd ⁡ ( m i , q ) = 1 for 1 ≤ i ≤ ℓ , and let n = m 1 + m 2 + ⋯ + m ℓ . Let Λ = ( λ 1 , λ 2 , ⋯ , λ ℓ ) be fixed, where λ 1 , λ 2 , ⋯ , λ ℓ are non-zero elements of F q . In this paper, we study the algebraic structure of Λ-multi-twisted codes of length n over F q and their dual codes with respect to the standard inner product on F q n . We provide necessary and sufficient conditions for the existence of a self-dual Λ-multi-twisted code of length n over F q , and obtain enumeration formulae for all self-dual and self-orthogonal Λ-multi-twisted codes of length n over F q . We also derive some sufficient conditions under which a Λ-multi-twisted code is linear with complementary dual (LCD). We determine the parity-check polynomial of all Λ-multi-twisted codes of length n over F q and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Λ-multi-twisted codes of length n over F q from the generating sets of the codes. Besides this, we provide a trace description for all Λ-multi-twisted codes of length n over F q by viewing these codes as direct sums of certain concatenated codes, which leads to a method to construct these codes. We also obtain a lower bound on their minimum Hamming distances using their multilevel concatenated structure.

      PubDate: 2018-02-25T16:00:54Z
      DOI: 10.1016/j.ffa.2018.01.012
      Issue No: Vol. 51 (2018)
       
  • Relative generalized Hamming weights of cyclic codes
    • Authors: Jun Zhang; Keqin Feng
      Pages: 338 - 355
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Jun Zhang, Keqin Feng
      Relative generalized Hamming weights (RGHWs) of a linear code with respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the linear codes. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems. In this paper, we investigate the RGHWs of cyclic codes of two nonzeros with respect to its irreducible cyclic subcodes. We give two formulae for RGHWs of the cyclic codes. As applications of the formulae, explicit examples are computed. Moreover, RGHWs of cyclic codes in the examples are very large, comparing with the generalized Plotkin bound of RGHWs. So it guarantees very high security for the secret sharing scheme based on the dual codes.

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.008
      Issue No: Vol. 50 (2018)
       
  • Preliminary results on the minimal polynomial of modified de Bruijn
           sequences
    • Authors: Lin Tan; Hong Xu; Wen-Feng Qi
      Pages: 356 - 365
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Lin Tan, Hong Xu, Wen-Feng Qi
      Modified de Bruijn sequences are created by removing a single zero from the longest run of zeros of de Bruijn sequences. There are few theoretical results on the minimal polynomial and linear complexity of modified de Bruijn sequences. Some preliminary results are presented in this paper. It shows that for the minimal polynomial of a modified de Bruijn sequence of order n there exists at least one irreducible factor of degree n. An equivalent condition on which a polynomial is the minimal polynomial of some modified de Bruijn sequence is derived, using the tool of rational fraction representation of periodic sequences. Based on the equivalent condition, the impossible linear complexity of modified de Bruijn sequences can be discussed.

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.007
      Issue No: Vol. 50 (2018)
       
  • Geometrically nilpotent subvarieties
    • Authors: Alexander Borisov
      Pages: 366 - 371
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Alexander Borisov
      We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several related open questions are stated and discussed.

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.009
      Issue No: Vol. 50 (2018)
       
  • The classification of antipodal two-weight linear codes
    • Authors: Dieter Jungnickel; Vladimir D. Tonchev
      Pages: 372 - 381
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Dieter Jungnickel, Vladimir D. Tonchev
      By a classical result of Bonisoli, the equidistant linear codes over GF ( q ) are, up to monomial equivalence, just the replications of some q-ary simplex code, possibly with added 0-coordinates. We prove an analogous result for the antipodal two-weight linear codes over GF ( q ) (that is, one of the two weights is the length of the code): up to monomial equivalence, any such code is ether a replication of a first order generalized Reed–Muller code, or a replication of a 3-dimensional projective code associated with some non-trivial maximal arc in the classical projective plane PG ( 2 , 2 s ) , s ≥ 1 . An equivalent geometric formulation of this result reads as follows: a multiset S of points spanning Π = PG ( m , q ) , m ≥ 2 , for which every hyperplane intersecting S does so in a constant number of points (counted with multiplicity), is either a multiple of a maximal arc in Π (for m = 2 ) or a multiple of the complement of some hyperplane of Π.

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.010
      Issue No: Vol. 50 (2018)
       
  • On the next-to-minimal weight of projective Reed–Muller codes
    • Authors: Cícero Carvalho; Victor G.L. Neumann
      Pages: 382 - 390
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Cícero Carvalho, Victor G.L. Neumann
      In this paper we present several values for the next-to-minimal weights of projective Reed–Muller codes. We work over F q with q ≥ 3 since in [3] we have determined the complete values for the next-to-minimal weights of binary projective Reed–Muller codes. As in [3] here we also find examples of codewords with next-to-minimal weight whose set of zeros is not in a hyperplane arrangement.

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.012
      Issue No: Vol. 50 (2018)
       
  • New 2-designs from strong difference families
    • Authors: Simone Costa; Tao Feng; Xiaomiao Wang
      Pages: 391 - 405
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Simone Costa, Tao Feng, Xiaomiao Wang
      Strong difference families will be used to get: seven 2-designs whose parameter sets were previously in doubt; a strong indication about the existence of 2- ( p q , p , 1 ) designs with p ∈ { 13 , 17 } and q a prime power; a better asymptotic bound on prime powers q for which there exists an ( F p × F q , F p × { 0 } , k , λ ) relative difference family with p a prime power and k ∈ { p , p + 1 } .

      PubDate: 2018-01-09T23:58:56Z
      DOI: 10.1016/j.ffa.2017.12.011
      Issue No: Vol. 50 (2018)
       
  • All α+uβ-constacyclic codes of length nps over Fpm+uFpm
    • Authors: Wei Zhao; Xilin Tang; Ze Gu
      Pages: 1 - 16
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Wei Zhao, Xilin Tang, Ze Gu
      Let F p m be a finite field with cardinality p m and R = F p m + u F p m with u 2 = 0 . We aim to determine all α + u β -constacyclic codes of length n p s over R, where α , β ∈ F p m ⁎ , n , s ∈ N + and gcd ⁡ ( n , p ) = 1 . Let α 0 ∈ F p m ⁎ and α 0 p s = α . The residue ring R [ x ] / 〈 x n p s − α − u β 〉 is a chain ring with the maximal ideal 〈 x n − α 0 〉 in the case that x n − α 0 is irreducible in F p m [ x ] . If x n − α 0 is reducible in F p m [ x ] , we give the explicit expressions of the ideals of R [ x ] / 〈 x n p s − α − u β 〉 . Besides, the number of codewords and the dual code of every α + u β -constacyclic code are provided.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.10.006
      Issue No: Vol. 50 (2017)
       
  • Some new results on the self-dual [120,60,24] code
    • Authors: Martino Borello; Javier de la Cruz
      Pages: 17 - 34
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Martino Borello, Javier de la Cruz
      The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further restrictions. Finally, we present some necessary conditions for the existence of the code, based on shadow and design theory.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.004
      Issue No: Vol. 50 (2017)
       
  • The arithmetic of consecutive polynomial sequences over finite fields
    • Authors: Domingo Gómez-Pérez; Alina Ostafe; Min Sha
      Pages: 35 - 65
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Domingo Gómez-Pérez, Alina Ostafe, Min Sha
      Motivated by a question of van der Poorten about the existence of an infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen consecutively from a sequence in a finite field of odd prime characteristic. We study the arithmetic of such sequences, including bounds for the largest degree of irreducible factors, the number of irreducible factors, as well as for the number of such sequences of fixed length in which all the polynomials are irreducible.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.002
      Issue No: Vol. 50 (2017)
       
  • Hartmann–Tzeng bound and skew cyclic codes of designed Hamming
           distance
    • Authors: José Gómez-Torrecillas; F.J. Lobillo; Gabriel Navarro; Alessando Neri
      Pages: 84 - 112
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): José Gómez-Torrecillas, F.J. Lobillo, Gabriel Navarro, Alessando Neri
      The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming distance is gained, and it is possible to design efficient decoding algorithms. In this paper, we give a version of the Hartmann–Tzeng bound that works for a wide class of skew cyclic codes. We also provide a practical method for constructing them with designed distance. For skew BCH codes, which are covered by our constructions, we discuss decoding algorithms. Detailed examples illustrate both the theory as the constructive methods it supports.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.001
      Issue No: Vol. 50 (2017)
       
  • The octonions as a twisted group algebra
    • Authors: Tathagata Basak
      Pages: 113 - 121
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Tathagata Basak
      We show that the octonions can be defined as the R -algebra with basis { e x : x ∈ F 8 } and multiplication given by e x e y = ( − 1 ) φ ( x , y ) e x + y , where φ ( x , y ) = tr ( y x 6 ) . While it is well known that the octonions can be described as a twisted group algebra, our purpose is to point out that this is a useful description. We show how the basic properties of the octonions follow easily from our definition. We give a uniform description of the sixteen orders of integral octonions containing the Gravesian integers, and a computation-free proof of their existence.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.003
      Issue No: Vol. 50 (2017)
       
  • Repeated-root two-dimensional constacyclic codes of length 2ps.2k
    • Authors: Zohreh Rajabi; Kazem Khashyarmanesh
      Pages: 122 - 137
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Zohreh Rajabi, Kazem Khashyarmanesh
      Let p be an odd prime. The main purpose of this paper is to establish and exploit the algebraic structure of some repeated-root two dimensional constacyclic codes of length 2 p s . 2 k over the finite field F p m . Moreover, we study all self-dual repeated-root two-dimensional ( λ , 1 ) -constacyclic codes of length 2 p s . 2 or 2 p s . 2 2 over F p m for λ ∈ { − 1 , 1 } .

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.008
      Issue No: Vol. 50 (2017)
       
  • Constructions of optimal LCD codes over large finite fields
    • Authors: Lin Sok; Minjia Shi; Patrick Solé
      Pages: 138 - 153
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Lin Sok, Minjia Shi, Patrick Solé
      In this paper 1 , we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.007
      Issue No: Vol. 50 (2017)
       
  • A class of new permutation trinomials
    • Authors: Ziran Tu; Xiangyong Zeng; Chunlei Li; Tor Helleseth
      Pages: 178 - 195
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ziran Tu, Xiangyong Zeng, Chunlei Li, Tor Helleseth
      In this paper, we characterize the coefficients of f ( x ) = x + a 1 x q ( q − 1 ) + 1 + a 2 x 2 ( q − 1 ) + 1 in F q 2 [ x ] for even q that lead f ( x ) to be a permutation of F q 2 . We transform the problem into studying some low-degree equations with variable in the unit circle, which are intensively investigated with some parameterization techniques. From the numerical results, the coefficients that lead f ( x ) to be a permutation appear to be completely characterized in this paper. It is also demonstrated that some permutations proposed in this paper are quasi-multiplicative (QM) inequivalent to the previously known permutation trinomials.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.009
      Issue No: Vol. 50 (2017)
       
  • Further results on permutation polynomials of the form
           (xpm−x+δ)s+x over Fp2m
    • Authors: Rohit Gupta; R.K. Sharma
      Pages: 196 - 208
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Rohit Gupta, R.K. Sharma
      Let F q denote the finite field of order q. In this paper, some new classes of permutation polynomials of the form ( x p m − x + δ ) s + x over F p 2 m are obtained by determining the number of solutions of certain equations.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.011
      Issue No: Vol. 50 (2017)
       
  • Strongly regular Cayley graphs from partitions of subdifference sets of
           the Singer difference sets
    • Authors: Koji Momihara; Qing Xiang
      Pages: 222 - 250
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Koji Momihara, Qing Xiang
      In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.ffa.2017.11.010
      Issue No: Vol. 50 (2017)
       
  • Pure Weierstrass gaps from a quotient of the Hermitian curve
    • Authors: Shudi Yang; Chuangqiang Hu
      Pages: 251 - 271
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Shudi Yang, Chuangqiang Hu
      In this paper, by employing some results on Kummer extensions, we give an arithmetic characterization of pure Weierstrass gaps at many totally ramified places on a quotient of the Hermitian curve, including the well-studied Hermitian curve as a special case. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results.

      PubDate: 2017-12-26T20:48:43Z
      DOI: 10.1016/j.ffa.2017.12.002
      Issue No: Vol. 50 (2017)
       
  • Normal bases and irreducible polynomials
    • Authors: Hua Huang; Shanmeng Han; Wei Cao
      Pages: 272 - 278
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Hua Huang, Shanmeng Han, Wei Cao
      A normal basis of F q n over F q is a basis of the form { α , α q , … , α q n − 1 } . An irreducible polynomial in F q [ x ] is called an N-polynomial if its roots are linearly independent over F q . Let p be the characteristic of F q . Pelis et al. showed that every monic irreducible polynomial with degree n and nonzero trace is an N-polynomial provided that n is either a power of p or a prime different from p and q is a primitive root modulo n. Chang et al. proved that the converse is also true. By comparing the number of N-polynomials with that of irreducible polynomials with nonzero traces, we present an alternative treatment to this problem and show that all the results mentioned above can be easily deduced from our main theorem.

      PubDate: 2017-12-26T20:48:43Z
      DOI: 10.1016/j.ffa.2017.12.004
      Issue No: Vol. 50 (2017)
       
  • Nilpotent linearized polynomials over finite fields and applications
    • Authors: Lucas Reis
      Pages: 279 - 292
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Lucas Reis
      Let q be a prime power and F q n be the finite field with q n elements, where n > 1 . We introduce the class of the linearized polynomials L ( X ) over F q n such that L ( t ) ( X ) : = L ∘ L ∘ ⋯ ∘ L ︸ t times ( X ) ≡ 0 ( mod X q n − X ) for some t ≥ 2 , called nilpotent linearized polynomials (NLP's). We discuss the existence and construction of NLP's and, as an application, we show how to obtain permutations of F q n from these polynomials. For some of those permutations, we can explicitly give the compositional inverse map and the cycle decomposition. This paper also contains a method for constructing involutions over binary fields with no fixed points, which are useful in block ciphers.

      PubDate: 2017-12-26T20:48:43Z
      DOI: 10.1016/j.ffa.2017.12.005
      Issue No: Vol. 50 (2017)
       
  • New permutation quadrinomials over F22m
    • Authors: Ziran Tu; Xiangyong Zeng; Tor Helleseth
      Pages: 304 - 318
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ziran Tu, Xiangyong Zeng, Tor Helleseth
      In this paper, we propose a class of permutation polynomials over the finite field F 2 2 m for odd m. These permutations are generally quadrinomials, and some permutation trinomials can also be obtained.

      PubDate: 2017-12-26T20:48:43Z
      DOI: 10.1016/j.ffa.2017.11.013
      Issue No: Vol. 50 (2017)
       
  • On period polynomials of degree 2m and weight distributions of certain
           irreducible cyclic codes
    • Authors: Ioulia N. Baoulina
      Pages: 319 - 337
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ioulia N. Baoulina
      We explicitly determine the values of reduced cyclotomic periods of order 2 m , m ≥ 4 , for finite fields of characteristic p ≡ 3  or  5 ( mod 8 ) . These evaluations are applied to obtain explicit factorizations of the corresponding reduced period polynomials. As another application, the weight distributions of certain irreducible cyclic codes are described.

      PubDate: 2017-12-26T20:48:43Z
      DOI: 10.1016/j.ffa.2017.12.006
      Issue No: Vol. 50 (2017)
       
  • Minimum distance and the minimum weight codewords of Schubert codes
    • Authors: Sudhir R. Ghorpade; Prasant Singh
      Pages: 1 - 28
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Sudhir R. Ghorpade, Prasant Singh
      We consider linear codes associated to Schubert varieties in Grassmannians. A formula for the minimum distance of these codes was conjectured in 2000 and after having been established in various special cases, it was proved in 2008 by Xiang. We give an alternative proof of this formula. Further, we propose a characterization of the minimum weight codewords of Schubert codes by introducing the notion of Schubert decomposable elements of certain exterior powers. It is shown that codewords corresponding to Schubert decomposable elements are of minimum weight and also that the converse is true in many cases. A lower bound, and in some cases, an exact formula, for the number of minimum weight codewords of Schubert codes is also given. From a geometric point of view, these results correspond to determining the maximum number of F q -rational points that can lie on a hyperplane section of a Schubert variety in a Grassmannian with its nondegenerate embedding in a projective subspace of the Plücker projective space, and also the number of hyperplanes for which the maximum is attained.

      PubDate: 2017-09-25T14:46:37Z
      DOI: 10.1016/j.ffa.2017.08.014
      Issue No: Vol. 49 (2017)
       
  • Formulas for roots of L-functions of the airy exponential sums
    • Authors: Hao Zhang
      Pages: 29 - 48
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Hao Zhang
      We study the L-function of the Airy exponential sum associated to the polynomial f ( X ) = X d + λ X using Dwork's dual theory on cohomology level. We get explicit formulas for all the roots of the L-function in the ordinary case in terms of p-adic GKZ-hypergeometric functions. Our method can also be used to give explicit formulas for all the roots of the L-function of the exponential sum associated to f ( X ) = X d + λ d − 1 X d − 1 + ⋯ + λ 0 .

      PubDate: 2017-09-25T14:46:37Z
      DOI: 10.1016/j.ffa.2017.09.004
      Issue No: Vol. 49 (2017)
       
  • Generalized Dedekind sums and the transformation formula in finite fields
    • Authors: Yoshinori Hamahata
      Pages: 49 - 61
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Yoshinori Hamahata
      We use periodic functions to introduce the generalized Dedekind sums in finite fields to describe the transformation formula for a family of certain functions.

      PubDate: 2017-09-25T14:46:37Z
      DOI: 10.1016/j.ffa.2017.09.005
      Issue No: Vol. 49 (2017)
       
  • Bilinear dual hyperovals from binary commutative presemifields II
    • Authors: Hiroaki Taniguchi
      Pages: 62 - 79
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Hiroaki Taniguchi
      We construct a bilinear dual hyperoval S c ( S 1 , S 2 , S 3 ) from binary commutative presemifields S 1 = ( G F ( q ) , + , ∘ ) and S 2 = ( G F ( q ) , + , ⁎ ) , a binary presemifield S 3 = ( G F ( q ) , + , ⋆ ) which may not be commutative, and a non-zero element c ∈ G F ( q ) which satisfies some conditions. We also determine the isomorphism problems under the conditions that S 1 and S 2 are not isotopic, and c ≠ 1 . We also investigate farther on the isomorphism problem on the case that S 1 and S 2 are the Kantor commutative presemifields and S 3 is the Albert presemifield.

      PubDate: 2017-10-02T04:29:38Z
      DOI: 10.1016/j.ffa.2017.08.009
      Issue No: Vol. 49 (2017)
       
  • The second largest number of points on plane curves over finite fields
    • Authors: Masaaki Homma; Seon Jeong Kim
      Pages: 80 - 93
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Masaaki Homma, Seon Jeong Kim
      A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree d over the finite field of q elements is also given for d ≥ q + 1 .

      PubDate: 2017-10-02T04:29:38Z
      DOI: 10.1016/j.ffa.2017.09.007
      Issue No: Vol. 49 (2017)
       
  • Distorting the volcano
    • Authors: Mireille Fouquet; Josep M. Miret; Javier Valera
      Pages: 108 - 125
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Mireille Fouquet, Josep M. Miret, Javier Valera
      Volcanoes of ℓ-isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ-isogenies, we present a condition over an endomorphism φ of E in order to determine which ℓ-isogenies of E are non-descending. The endomorphism φ is defined as the crater cycle of an m-volcano where E is located, with m ≠ ℓ . The condition is feasible when φ is a distortion map for a subgroup of order ℓ of E. We also provide some relationships among the crater sizes of volcanoes of m-isogenies whose elliptic curves belong to a volcano of ℓ-isogenies.

      PubDate: 2017-10-02T04:29:38Z
      DOI: 10.1016/j.ffa.2017.09.006
      Issue No: Vol. 49 (2017)
       
  • On permutation trinomials of type x2ps+r+xps+r+λxr
    • Authors: Daniele Bartoli; Giovanni Zini
      Pages: 126 - 131
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Daniele Bartoli, Giovanni Zini
      We determine all permutation trinomials of type x 2 p s + r + x p s + r + λ x r over the finite field F p t when ( 2 p s + r ) 4 < p t . This partially extends a previous result by Bhattacharya and Sarkar in the case p = 2 , r = 1 .

      PubDate: 2017-10-10T07:13:15Z
      DOI: 10.1016/j.ffa.2017.09.010
      Issue No: Vol. 49 (2017)
       
  • Kronecker–Halton sequences in Fp((X−1))
    • Authors: Roswitha Hofer
      Pages: 23 - 29
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Roswitha Hofer
      In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.

      PubDate: 2017-12-13T06:22:49Z
      DOI: 10.1016/j.jco.2017.09.001
      Issue No: Vol. 44 (2017)
       
  • Some new non-additive maximum rank distance codes
    • Authors: Kamil Otal; Ferruh
      Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Kamil Otal, Ferruh Özbudak
      In this paper, a construction of maximum rank distance (MRD) codes as a generalization of generalized Gabidulin codes is given. The family of the resulting codes is not covered properly by additive generalized twisted Gabidulin codes, and does not cover all twisted Gabidulin codes. When the basis field has more than two elements, this family includes also non-affine MRD codes, and such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters.

      PubDate: 2017-12-26T20:48:43Z
       
  • Codes over affine algebras with a finite commutative chain coefficient
           ring
    • Authors: I.F.
      Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): E. Martínez-Moro, A. Piñera-Nicolás, I.F. Rúa
      We consider codes defined over an affine algebra A = R [ X 1 , … , X r ] / 〈 t 1 ( X 1 ) , … , t r ( X r ) 〉 , where t i ( X i ) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A − submodules of A l ( l ∈ N ). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain rings. Some codes over Frobenius local rings that are not chain rings are also of this type. A canonical generator matrix for these codes is introduced with the help of the Canonical Generating System. Duality of the codes is also considered.

      PubDate: 2017-10-02T04:29:38Z
       
 
 
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