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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (651 journals)
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MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
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: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
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: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
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 Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
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: 7)
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: 3)
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: 9)
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: 6)
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)
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: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
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  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access  
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: 7)
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 the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
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  
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: 2)
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: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
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: 9)
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: 4)
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: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Finite Fields and Their Applications
  [SJR: 1.096]   [H-I: 29]   [4 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 1071-5797 - ISSN (Online) 1090-2465
   Published by Elsevier Homepage  [3043 journals]
  • Invariants of trace forms in odd characteristic and authentication codes
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Robert W. Fitzgerald, Yasanthi Kottegoda
      We complete A. Klapper's work on the invariant of a one-term trace form over a finite field of odd characteristic. We apply this to computing the probability of a successful impersonation attack on an authentication code proposed by C. Ding et al. (2005).

      PubDate: 2017-07-28T01:11:13Z
       
  • Power sums over finite commutative unital rings
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): José María Grau, Antonio M. Oller-Marcén
      In this paper we compute the sum of the k-th powers of all the elements of a finite commutative unital ring, thus generalizing known results for finite fields, the rings of integers modulo n or the ring of Gaussian integers modulo n. As an application, we focus on quotient rings of the form ( Z / n Z ) [ x ] / ( f ( x ) ) for a polynomial f ∈ Z [ x ] .

      PubDate: 2017-07-28T01:11:13Z
       
  • Ambiguity, deficiency and differential spectrum of normalized permutation
           polynomials over finite fields
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Daniel Panario, Daniel Santana, Qiang Wang
      We obtain exact formulas for the differential spectrum, deficiency and ambiguity of all normalized permutation polynomials of degree up to six over finite fields.

      PubDate: 2017-07-28T01:11:13Z
       
  • Curves of medium genus with many points
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Everett W. Howe
      The defect of a curve over a finite field is the difference between the number of rational points on the curve and the Weil–Serre upper bound for the number of points on the curve. We present algorithms for constructing curves of genus 5, 6, and 7 with small defect. Our aim is to be able to produce, in a reasonable amount of time, curves that can be used to populate the online table of curves with many points found at manypoints.org .

      PubDate: 2017-07-21T13:39:38Z
       
  • A q-polynomial approach to constacyclic codes
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Weijun Fang, Jiejing Wen, Fang-Wei Fu
      As a generalization of cyclic codes, constacyclic codes is an important and interesting class of codes due to their nice algebraic structures and various applications in engineering. This paper is devoted to the study of the q-polynomial approach to constacyclic codes. Fundamental theory of this approach will be developed, and will be employed to construct some families of optimal and almost optimal codes in this paper.

      PubDate: 2017-07-21T13:39:38Z
       
  • Structure and performance of generalized quasi-cyclic codes
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Cem Güneri, Ferruh Özbudak, Buket Özkaya, Elif Saçıkara, Zahra Sepasdar, Patrick Solé
      Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that are LCD, but not QC, are exhibited.

      PubDate: 2017-07-21T13:39:38Z
       
  • A generalization of the Hasse–Witt matrix of a hypersurface
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Alan Adolphson, Steven Sperber
      The Hasse–Witt matrix of a hypersurface in P n over a finite field of characteristic p gives essentially complete mod p information about the zeta function of the hypersurface. But if the degree d of the hypersurface is ≤n, the zeta function is trivial mod p and the Hasse–Witt matrix is zero-by-zero. We generalize a classical formula for the Hasse–Witt matrix to obtain a matrix that gives a nontrivial congruence for the zeta function for all d. We also describe the differential equations satisfied by this matrix and prove that it is generically invertible.

      PubDate: 2017-07-21T13:39:38Z
       
  • Discrete linear models for the generalized self-shrunken sequences
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Sara D. Cardell, Amparo Fúster-Sabater
      In this work, different decimation-based sequence generators for cryptographic purposes have been analyzed in detail. In fact, the modified self-shrinking generator was first introduced as an improved version of the self-shrinking generator. However, it is here proven that the sequences produced by both generators belong to the same family of sequences, that is the class of the generalized self-shrinking sequences. Thus, both sequences have the same properties as well as the same weaknesses. Moreover, such sequences can be generated by linear structures based on one-dimensional cellular automata. The linearity inherent to the cellular automata-based models can be used to launch a cryptanalytic attack against such non-linear generators.

      PubDate: 2017-07-21T13:39:38Z
       
  • Counting perfect polynomials
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): U. Caner Cengiz, Paul Pollack, Enrique Treviño
      Let A ∈ F 2 [ T ] . We say A is perfect if A coincides with the sum of all of its divisors in F 2 [ T ] . We prove that the number of perfect polynomials A with A ≤ x is O ϵ ( x 1 / 12 + ϵ ) for all ϵ > 0 , where A = 2 deg ⁡ A . We also prove that every perfect polynomial A with 1 < A ≤ 1.6 × 10 60 is divisible by T or T + 1 ; that is, there are no small “odd” perfect polynomials.

      PubDate: 2017-07-21T13:39:38Z
       
  • Permutation polynomials over F2n of the form
           (x2i+x+δ)s1+(x2i+x+δ)s2+x
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Xiangyong Zeng, Xishun Zhu, Nian Li, Xianping Liu
      Permutation polynomials having the form ( x 2 i + x + δ ) s 1 + ( x 2 i + x + δ ) s 2 + x over finite fields of even characteristic are investigated in this paper. Eight classes of such polynomials are proved to be permutations.

      PubDate: 2017-07-21T13:39:38Z
       
  • Quartic polynomials having Galois closure of genus zero and their value
           sets
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Robert C. Valentini
      Let v be the number of distinct values of the polynomial f ( x ) = x 4 + a x 2 + b x , where a and b are elements of the finite field k of size q, where q is odd. When b is 0, an exact formula for v can be given. When b is not 0, as a consequence of the Tchebotarev Density Theorem, v = ( 5 / 8 ) q + O ( q ) . When the Galois closure of k ( x ) / k ( f ( x ) ) is a rational function field, v can be determined exactly. In this work we determine those f ( x ) 's for which this occurs and give the formula for v.

      PubDate: 2017-07-21T13:39:38Z
       
  • On maximal cliques of polar graphs
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Antonio Cossidente, Giuseppe Marino, Francesco Pavese
      The maximal cliques of the graph NU ( 4 , q 2 ) related to the Hermitian surface of PG ( 3 , q 2 ) and of the graph NO ± ( 2 n + 2 , q ) , q even, n ≥ 1 , are classified.

      PubDate: 2017-07-21T13:39:38Z
       
  • The Galois variance of constacyclic codes
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Thomas Blackford
      This paper studies the Galois images of constacyclic codes over F q m of length relatively prime to q, and determines when those images are equal and when they intersect only at the zero codeword. The subfield subcodes and trace codes of constacyclic codes are also determined.

      PubDate: 2017-07-21T13:39:38Z
       
  • On the construction of differentially 4-uniform involutions
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Yuwei Xu, Yongqiang Li, Chuankun Wu, Feng Liu
      An involution is a permutation whose compositional inverse is itself. Differentially 4-uniform involutions with high algebraic degree and high nonlinearity are important for the design of block ciphers because they possess good cryptographic properties and the same component can be used in both encryption circuit and decryption circuit. A well known differentially 4-uniform involution is the multiplicative inverse function, which is used as the S-boxes in AES and Camellia. Although many differential 4-uniform permutations have been constructed, there are only a few classes of differentially 4-uniform involutions. Recently, Charpin et al. presented an idea of constructing involutions, which is called piece by piece construction. With this method, we construct a family of differentially 4-uniform involutions with optimal algebraic degree and high nonlinearity. It is also shown with the help of computer that such involutions which are CCZ-inequivalent to the known differentially 4-uniform permutations in small number of even dimensions are constructed. Furthermore, the number of CCZ-inequivalent classes of our involutions over F 2 n increases exponentially when n increases.

      PubDate: 2017-07-21T13:39:38Z
       
  • Enumerating permutation polynomials
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Theodoulos Garefalakis, Giorgos Kapetanakis
      We consider the problem of enumerating polynomials over F q , that have certain coefficients prescribed to given values and permute certain substructures of F q . In particular, we are interested in the group of N-th roots of unity and in the submodules of F q . We employ the techniques of Konyagin and Pappalardi to obtain results that are similar to their results in Konyagin and Pappalardi (2006) [8]. As a consequence, we prove conditions that ensure the existence of low-degree permutation polynomials of the mentioned substructures of F q .

      PubDate: 2017-07-08T03:19:27Z
       
  • Bent functions and line ovals
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Kanat Abdukhalikov
      In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also show that bent functions which are linear on elements of inequivalent spreads can be EA-equivalent.

      PubDate: 2017-07-08T03:19:27Z
       
  • G2 and some exceptional Witt vector identities
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Nicholas M. Katz
      We find some new one-parameter families of exponential sums in every odd characteristic whose geometric and arithmetic monodromy groups are G 2 .

      PubDate: 2017-07-08T03:19:27Z
       
  • Plateaudness of Kasami APN functions
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Satoshi Yoshiara
      It is shown that the Kasami function defined on F 2 n with n even is plateaued. This generalizes a result [3, Theorem 11], where the restriction ( n , 3 ) = 1 is assumed. The result is used to establish the CCZ-inequivalence of the Kasami function defined on F 2 n with n even to the other known monomial APN functions [4].

      PubDate: 2017-06-09T22:57:53Z
       
  • On the multiplicative order of the roots of bXqr+1−aXqr+dX−c
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): F.E. Brochero Martínez, Theodoulos Garefalakis, Lucas Reis, Eleni Tzanaki
      In this paper, we find a lower bound for the order of the group 〈 θ + α 〉 ⊂ F ‾ q ⁎ , where α ∈ F q , θ is a generic root of the polynomial F A , r ( X ) = b X q r + 1 − a X q r + d X − c ∈ F q [ X ] and a d − b c ≠ 0 .

      PubDate: 2017-06-09T22:57:53Z
       
  • Code generator matrices as RNG conditioners
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): A. Tomasi, A. Meneghetti, M. Sala
      We quantify precisely the distribution of the output of a binary random number generator (RNG) after conditioning with a binary linear code generator matrix by showing the connection between the Walsh spectrum of the resulting random variable and the weight distribution of the code. Previously known bounds on the performance of linear binary codes as entropy extractors can be derived by considering generator matrices as a selector of a subset of that spectrum. We also extend this framework to the case of non-binary codes.

      PubDate: 2017-06-09T22:57:53Z
       
  • A generalization of APN functions for odd characteristic
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Masamichi Kuroda, Shuhei Tsujie
      Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on. However, APN functions on finite fields of odd characteristic do not satisfy desired properties. In this paper, we modify the definition of APN function in the case of odd characteristic, and study its properties.

      PubDate: 2017-06-09T22:57:53Z
       
  • On two conjectures about permutation trinomials over F32k
    • Abstract: Publication date: September 2017
      Source:Finite Fields and Their Applications, Volume 47
      Author(s): Nian Li
      Permutation polynomials with a few terms attract researchers' interest in recent years due to their simple algebraic form and some additional extraordinary properties. In this paper, by analyzing the quadratic factors of a fifth-degree polynomial and a seventh-degree polynomial over the finite field F 3 2 k , two conjectures on permutation trinomials over F 3 2 k proposed recently by Li, Qu, Li and Fu are settled, where k is a positive integer.

      PubDate: 2017-06-04T21:49:05Z
       
  • Construction of some new quantum MDS codes
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Xueying Shi, Qin Yue, Xiaomeng Zhu
      Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, we mainly apply a new method of classical Hermitian self-orthogonal codes to construct three classes of new quantum MDS codes, and these quantum MDS codes provide large minimum distance.

      PubDate: 2017-05-25T20:21:01Z
       
  • Measure-preservation criteria for 1-Lipschitz functions on Fq[[T]] in
           terms of the three bases of Carlitz polynomials, digit derivatives, and
           digit shifts
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Youngho Jang, Sangtae Jeong, Chunlan Li
      As a follow-up to our previous work [10], we characterize the measure-preservation of 1-Lipschitz functions on F q [ [ T ] ] in terms of the three well-known bases: Carlitz polynomials, digit derivatives, and digit shifts.

      PubDate: 2017-05-20T16:15:24Z
       
  • Matroidal structure of skew polynomial rings with application to network
           coding
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Siyu Liu, Felice Manganiello, Frank R. Kschischang
      Over a finite field F q m , the evaluation of skew polynomials is intimately related to the evaluation of linearized polynomials. This connection allows one to relate the concept of polynomial independence defined for skew polynomials to the familiar concept of linear independence for vector spaces. This relation allows for the definition of a representable matroid called the F q m [ x ; σ ] -matroid, with rank function that makes it a metric space. Specific submatroids of this matroid are individually bijectively isometric to the projective geometry of F q m equipped with the subspace metric. This isometry allows one to use the F q m [ x ; σ ] -matroid in a matroidal network coding application.

      PubDate: 2017-05-20T16:15:24Z
       
  • n×1 local gamma factors and Gauss sums
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Chufeng Nien
      This paper relates n × 1 local gamma factors over finite fields with Gauss sums and characterizes F q × -distinguished characters of F q 2 × in terms of special values of twisted local gamma factors.

      PubDate: 2017-04-30T08:06:25Z
       
  • New extremal binary self-dual codes of lengths 64 and 66 from R2-lifts
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Abidin Kaya
      Recently, Karadeniz and Yildiz introduced an efficient method to search for self-dual codes. It is called lifting method and can be applied to some alphabets. In this work, by considering R 2 -lifts of binary self-dual codes of length 16 new extremal binary self-dual codes of lengths 64 are constructed as Gray images. More precisely, we construct 15 new codes of length 64. Moreover, 10 new codes of length 66 were obtained by applying a building-up construction to the binary codes. Codes with these weight enumerators are constructed for the first time in the literature. The results are tabulated.

      PubDate: 2017-04-30T08:06:25Z
       
  • Existence of some special primitive normal elements over finite fields
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Anju, R.K. Sharma
      In this article, we establish a sufficient condition for the existence of a primitive element α ∈ F q such that for any matrix ( a b c 0 d e ) ∈ M 2 × 3 ( F q ) of rank 2, the element ( a α 2 + b α + c ) / ( d α + e ) is a primitive element of F q , where q = 2 k for some positive integer k. We also give a sufficient condition for the existence of a primitive normal element α ∈ F q n over F q such that ( a α 2 + b α + c ) / ( d α + e ) is a primitive element of F q n for every matrix ( a b c 0 d e ) ∈ M 2 × 3 ( F q n ) of rank 2.

      PubDate: 2017-04-30T08:06:25Z
       
  • Bent and bent4 spectra of Boolean functions over finite fields
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Nurdagül Anbar, Wilfried Meidl
      For c ∈ F 2 n , a c-bent4 function f from the finite field F 2 n to F 2 is a function with a flat spectrum with respect to the unitary transform V f c , which is designed to describe the component functions of modified planar functions. For c = 0 the transform V f c reduces to the conventional Walsh transform, and hence a 0-bent4 function is bent. In this article we generalize the concept of partially bent functions to the transforms V f c . We show that every quadratic function is partially bent, and hence it is plateaued with respect to any of the transforms V f c . In detail we analyse two quadratic monomials. The first has values as small as possible in its spectra with respect to all transforms V f c , and the second has a flat spectrum for a large number of c. Moreover, we show that every quadratic function is c-bent4 for at least three distinct c. In the last part we analyse a cubic monomial. We show that it is c-bent4 only for c = 1 , the function is then called negabent, which shows that non-quadratic functions exhibit a different behaviour.

      PubDate: 2017-04-23T07:06:14Z
       
  • Supercongruences involving dual sequences
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Zhi-Wei Sun
      In this paper we study some sophisticated supercongruences involving dual sequences. For n = 0 , 1 , 2 , … define d n ( x ) = ∑ k = 0 n ( n k ) ( x k ) 2 k and s n ( x ) = ∑ k = 0 n ( n k ) ( x k ) ( x + k k ) = ∑ k = 0 n ( n k ) ( − 1 ) k ( x k ) ( − 1 − x k ) . For any odd prime p and p-adic integer x, we determine ∑ k = 0 p − 1 ( ± 1 ) k d k ( x ) 2 and ∑ k = 0 p − 1 ( 2 k + 1 ) d k ( x ) 2 modulo p 2 ; for example, we establish the new p-adic congruence ∑ k = 0 p − 1 ( − 1 ) k d k ( x ) 2 ≡ ( − 1 ) 〈 x 〉 p ( mod p 2 ) , where 〈 x 〉 p denotes the least nonnegative integer r with x ≡ r ( mod p ) . For any prime p > 3 and p-adic integer x, we determine
      PubDate: 2017-04-23T07:06:14Z
       
  • A novel approach for constructing reversible codes and applications to DNA
           codes over the ring F2[u]/(u2k−1)
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Elif Segah Oztas, Bahattin Yildiz, Irfan Siap
      In this work we introduce a novel approach to find reversible codes over different alphabets, using so-called coterm polynomials and a module-construction. We obtain many optimal reversible codes with these constructions. In an attempt to apply the constructions to the DNA, we identify k-bases of DNA with elements in the ring R 2 k = F 2 [ u ] / ( u 2 k − 1 ) , and by using a form of coterm polynomials, we are able to solve the reversibility and complement problems in DNA codes over this ring. With a freedom on the choice of k we are able to embed any DNA code in a suitable ring, giving an algebraic structure to the DNA codes. We are also able to find reversible and reversible-complement codes that are not necessarily linear cyclic codes.

      PubDate: 2017-04-23T07:06:14Z
       
  • A note on character sums in finite fields
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Abhishek Bhowmick, Thái Hoàng Lê, Yu-Ru Liu
      We prove a character sum estimate in F q [ t ] and answer a question of Shparlinski.

      PubDate: 2017-04-23T07:06:14Z
       
  • Chow's theorem for linear codes
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Mariusz Kwiatkowski, Mark Pankov
      Let Γ k ( V ) be the Grassmann graph formed by k-dimensional subspaces of an n-dimensional vector space over the finite field F q consisting of q elements and 1 < k < n − 1 . Denote by Γ ( n , k ) q the restriction of the Grassmann graph to the set of all non-degenerate linear [ n , k ] q codes. We describe maximal cliques of the graph Γ ( n , k ) q and show that every automorphism of this graph is induced by a monomial semilinear automorphism of V.

      PubDate: 2017-04-15T18:06:23Z
       
  • Perfect codes in poset spaces and poset block spaces
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): B.K. Dass, Namita Sharma, Rashmi Verma
      The paper begins by giving a counter example to show that the algorithm for construction of new perfect poset codes from a given perfect poset code by removal of a coordinate as given by Lee (2004) [11] does not hold. The algorithm has been improved and generalized to obtain new perfect poset block codes from a given perfect poset block code. The modified necessary and sufficient conditions for the construction of new perfect poset codes have been derived as a particular case. A bound has been obtained on the height of poset P s that turns a given π-code into r-perfect ( P s , π ) -code. We show that there does not exist a poset which admits the binary Simplex code of order 3 to be a 2-perfect poset code. Also, all the poset structures which admit the extended ternary Golay code to be a 3-perfect poset code have been classified.

      PubDate: 2017-04-09T17:11:24Z
       
  • Enumerative coding for line polar Grassmannians with applications to codes
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Ilaria Cardinali, Luca Giuzzi
      A k-polar Grassmannian is a geometry having as pointset the set of all k-dimensional subspaces of a vector space V which are totally isotropic for a given non-degenerate bilinear form μ defined on V. Hence it can be regarded as a subgeometry of the ordinary k-Grassmannian. In this paper we deal with orthogonal line Grassmannians and with symplectic line Grassmannians, i.e. we assume k = 2 and μ to be a non-degenerate symmetric or alternating form. We will provide a method to efficiently enumerate the pointsets of both orthogonal and symplectic line Grassmannians. This has several nice applications; among them, we shall discuss an efficient encoding/decoding/error correction strategy for line polar Grassmann codes of either type.

      PubDate: 2017-04-09T17:11:24Z
       
  • A note on APN permutations in even dimension
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): M. Calderini, M. Sala, I. Villa
      APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In particular, we prove that none of their components can be quadratic. For an APN vectorial Boolean function (in even dimension) with all cubic components we prove the existence of a component having a large number of balanced derivatives. Using these restrictions, we obtain the first theoretical proof of the non-existence of APN permutations in dimension 4. Moreover, we derive some constraints on APN permutations in dimension 6.

      PubDate: 2017-03-25T14:52:16Z
       
  • Three-weight ternary linear codes from a family of power functions
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Yongbo Xia, Chunlei Li
      Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined by studying the properties of some exponential sums related to the power functions.

      PubDate: 2017-03-25T14:52:16Z
       
  • Permutation trinomials over F2m
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Danyao Wu, Pingzhi Yuan, Cunsheng Ding, Yuzhen Ma
      Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we determine all permutation trinomials over F 2 m in Zieve's paper [30]. We prove a conjecture proposed by Gupta and Sharma in [8] and obtain some new permutation trinomials over F 2 m . Finally, we show that some classes of permutation trinomials with parameters are QM equivalent to some known permutation trinomials.

      PubDate: 2017-03-25T14:52:16Z
       
  • New explicit binary constant weight codes from Reed–Solomon codes
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Liqing Xu, Hao Chen
      Binary constant weight codes have important applications in various topics and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose an improvement of the Ericson–Zinoviev construction of binary constant weight codes from q-ary codes. By applying this improvement to Reed–Solomon codes, some new or optimal binary constant weight codes are presented. In particular new binary constant weight codes A ( 64 , 10 , 8 ) ≥ 4112 and A ( 64 , 12 , 8 ) ≥ 522 are constructed. We also give explicitly constructed binary constant weight codes which improve the Gilbert and the Graham–Sloane lower bounds asymptotically in a small range of parameters. Some new binary constant weight codes constructed from algebraic-geometric codes by applying our this improvement are also presented.

      PubDate: 2017-03-25T14:52:16Z
       
  • On the girth of Tanner (3,11) quasi-cyclic LDPC codes
    • Abstract: Publication date: July 2017
      Source:Finite Fields and Their Applications, Volume 46
      Author(s): Hengzhou Xu, Baoming Bai, Dan Feng, Cheng Sun
      Motivated by the works on the girth of Tanner ( 3 , 5 ) and ( 3 , 7 ) quasi-cyclic (QC) low-density parity-check (LDPC) codes done by S. Kim et al. and M. Gholami et al., respectively, we analyze the cycles of Tanner ( 3 , 11 ) QC LDPC codes and present the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner ( 3 , 11 ) QC LDPC codes. By checking these conditions, the girth values of Tanner ( 3 , 11 ) QC LDPC codes are derived.

      PubDate: 2017-03-25T14:52:16Z
       
 
 
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