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  Subjects -> MATHEMATICS (Total: 886 journals)
    - APPLIED MATHEMATICS (72 journals)
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    - MATHEMATICS (656 journals)
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MATHEMATICS (656 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: 3)
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: 22)
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: 8)
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: 5)
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: 2)
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: 6)
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: 8)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
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   (Followers: 1)
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: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
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   (Followers: 1)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 8)
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: 20)
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: 3)
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: 28)
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: 8)
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: 5)
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)

        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]
  • Carlitz rank and index of permutation polynomials
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Leyla Işık, Arne Winterhof
      Carlitz rank and index are two important measures for the complexity of a permutation polynomial f ( x ) over the finite field F q . In particular, for cryptographic applications we need both, a high Carlitz rank and a high index. In this article we study the relationship between Carlitz rank C r k ( f ) and index I n d ( f ) . More precisely, if the permutation polynomial is neither close to a polynomial of the form ax nor a rational function of the form a x − 1 , then we show that C r k ( f ) > q − max ⁡ { 3 I n d ( f ) , ( 3 q ) 1 / 2 } . Moreover we show that the permutation polynomial which represents the discrete logarithm guarantees both a large index and a large Carlitz rank.

      PubDate: 2017-10-14T08:44:07Z
       
  • On permutation trinomials of type x2ps+r+xps+r+λxr
    • 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
       
  • On the difference between permutation polynomials
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Nurdagül Anbar, Almasa Odz̆ak, Vandita Patel, Luciane Quoos, Anna Somoza, Alev Topuzoğlu
      The well-known Chowla and Zassenhaus conjecture, proved by Cohen in 1990, states that if p > ( d 2 − 3 d + 4 ) 2 , then there is no complete mapping polynomial f in F p [ x ] of degree d ≥ 2 . For arbitrary finite fields F q , a similar non-existence result was obtained recently by Işık, Topuzoğlu and Winterhof in terms of the Carlitz rank of f. Cohen, Mullen and Shiue generalized the Chowla–Zassenhaus–Cohen Theorem significantly in 1995, by considering differences of permutation polynomials. More precisely, they showed that if f and f + g are both permutation polynomials of degree d ≥ 2 over F p , with p > ( d 2 − 3 d + 4 ) 2 , then the degree k of g satisfies k ≥ 3 d / 5 , unless g is constant. In this article, assuming f and f + g are permutation polynomials in F q [ x ] , we give lower bounds for the Carlitz rank of f in terms of q and k. Our results generalize the above mentioned result of Işık et al. We also show for a special class of permutation polynomials f of Carlitz rank n ≥ 1 that if f + x k is a permutation over F q , with gcd ⁡ ( k + 1 , q − 1 ) = 1 , then k ≥ ( q − n ) / ( n + 3 ) .

      PubDate: 2017-10-10T07:13:15Z
       
  • Bivariate identities related to Chebyshev and Dickson polynomials over Fq
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Ron Evans, Mark Van Veen
      Let F q be a field of q elements, where q is a power of an odd prime p. The polynomial f ( y ) ∈ F q [ y ] defined by f ( y ) : = ( 1 + y ) ( q + 1 ) / 2 + ( 1 − y ) ( q + 1 ) / 2 has the property that f ( 1 − y ) = ρ ( 2 ) f ( y ) , where ρ is the quadratic character on F q . This univariate identity was applied to prove a recent theorem of N. Katz. We formulate and prove a bivariate extension, and give an application to quadratic residuacity.

      PubDate: 2017-10-10T07:13:15Z
       
  • Bilinear dual hyperovals from binary commutative presemifields II
    • 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
       
  • The second largest number of points on plane curves over finite fields
    • 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
       
  • Codes over affine algebras with a finite commutative chain coefficient
           ring
    • 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
       
  • Distorting the volcano
    • 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
       
  • Minimum distance and the minimum weight codewords of Schubert codes
    • 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
       
  • Formulas for roots of L-functions of the airy exponential sums
    • 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
       
  • Generalized Dedekind sums and the transformation formula in finite fields
    • 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
       
  • On the irreducibility of Fibonacci and Lucas polynomials over finite
           fields
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Hidetaka Kitayama, Daisuke Shiomi
      In this paper, we give the necessary and sufficient condition that Fibonacci and Lucas polynomials are irreducible in F q [ T ] . As applications of our results, under the GRH, we prove that there are infinitely many irreducible Fibonacci and Lucas polynomials in F q [ T ] for some q.

      PubDate: 2017-09-18T13:18:09Z
       
  • Duplication free public keys based on SIS-type problems
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Hyang-Sook Lee, Juhee Lee, Seongan Lim
      In the public key cryptography, we say that two public keys are duplicated if they share a private key in common. We point out that no duplicate public keys exist in the RSA public key scheme since there is a one-to-one correspondence between the set of problems and the set of solutions for integer factorization problem. Contrary to the integer factorization problem, there is no such one-to-one correspondence with Short Integer Solution (SIS)-type problems and this necessitates to study its effect on duplicate public keys of the schemes based on SIS. In this paper, we analyze the existence of duplicate public keys with four types of SIS problem: SIS, SIS with full rank solution set, basic Inhomogeneous SIS (ISIS), ISIS with the defining matrix A as a public parameter. As a result, we show that there is no provable way to exclude duplicate public keys of the schemes based on the basic SIS, basic ISIS, and SIS with a full rank solution set. However, we show that if A is given in the systematic form and the given set of solutions forms a matrix of rank ( m − n ) over Z q , then it guarantees duplication free public keys. We also prove that the schemes based on ISIS with the matrix A as a public parameter always guarantee duplication free public keys.

      PubDate: 2017-09-18T13:18:09Z
       
  • A strongly regular decomposition of the complete graph and its association
           scheme
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Hadi Kharaghani, Sara Sasani, Sho Suda
      For any positive integer m, the complete graph on 2 2 m ( 2 m + 2 ) vertices is decomposed into 2 m + 1 commuting strongly regular graphs, which give rise to a symmetric association scheme of class 2 m + 2 − 2 . Furthermore, the eigenmatrices of the symmetric association schemes are determined explicitly. As an application, the eigenmatrix of the commutative strongly regular decomposition obtained from the strongly regular graphs is derived.

      PubDate: 2017-09-12T09:17:53Z
       
  • Locality of optimal binary codes
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Qiang Fu, Ruihu Li, Luobin Guo, Liangdong Lv
      The locality of locally repairable codes (LRCs) for a distributed storage system is the number of nodes that participate in the repair of failed nodes, which characterizes the repair cost. In this paper, we first determine the locality of MacDonald codes, then propose three constructions of LRCs with r = 1 , 2  and  3 . Based on these results, for 2 ≤ k ≤ 7 and n ≥ k + 2 , we give an optimal linear [ n , k , d ] code with small locality. The distance optimality of these linear codes can be judged by the codetable of M. Grassl for n < 2 ( 2 k − 1 ) and by the Griesmer bound for n ≥ 2 ( 2 k − 1 ) . Almost all the [ n , k , d ] codes ( 2 ≤ k ≤ 7 ) have locality r ≤ 3 except for the three codes, and most of the [ n , k , d ] code with n < 2 ( 2 k − 1 ) achieves the Cadambe–Mazumdar bound for LRCs.

      PubDate: 2017-09-12T09:17:53Z
       
  • Number of points of a nonsingular hypersurface in an odd-dimensional
           projective space
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Masaaki Homma, Seon Jeong Kim
      The numbers of F q -points of nonsingular hypersurfaces of a fixed degree in an odd-dimensional projective space are investigated, and an upper bound for them is given. Also we give the complete list of nonsingular hypersurfaces each of which realizes the upper bound. This is a natural generalization of our previous study of surfaces in projective 3-space.

      PubDate: 2017-09-12T09:17:53Z
       
  • Corrigendum to “Toric codes and finite geometries” [Finite Fields
           Appl. 45 (2017) 203–216]
    • Abstract: Publication date: Available online 11 September 2017
      Source:Finite Fields and Their Applications
      Author(s): John B. Little
      This correction adds a necessary hypothesis in Proposition 2.4 of [1]. A counterexample to the previous version was pointed out to the author by Melda Görür and the author thanks her for bringing that to his attention. Theorem 3.2 and Corollary 3.3 are also reformulated so they do not refer to the new, more restricted Proposition 2.4.

      PubDate: 2017-09-12T09:17:53Z
       
  • Generalizations of self-reciprocal polynomials
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Sandro Mattarei, Marco Pizzato
      A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of irreducible polynomials arising through an arbitrary quadratic transformation. In the present paper we provide an explanation for this extension, and a simpler proof of Ahmadi's result, by a reduction to the known special case of self-reciprocal polynomials and a minor variation. We also prove further results on polynomials arising through a quadratic transformation, and through some special transformations of higher degree.

      PubDate: 2017-09-06T08:02:15Z
       
  • An Appell series over finite fields
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Bing He, Long Li, Ruiming Zhang
      In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.

      PubDate: 2017-09-06T08:02:15Z
       
  • On s-extremal singly even self-dual [24k+8,12k+4,4k+2] codes
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Masaaki Harada, Akihiro Munemasa
      A relationship between s-extremal singly even self-dual [ 24 k + 8 , 12 k + 4 , 4 k + 2 ] codes and extremal doubly even self-dual [ 24 k + 8 , 12 k + 4 , 4 k + 4 ] codes with covering radius meeting the Delsarte bound, is established. As an example of the relationship, s-extremal singly even self-dual [ 56 , 28 , 10 ] codes are constructed for the first time. In addition, we show that there is no extremal doubly even self-dual code of length 24 k + 8 with covering radius meeting the Delsarte bound for k ≥ 137 . Similarly, we show that there is no extremal doubly even self-dual code of length 24 k + 16 with covering radius meeting the Delsarte bound for k ≥ 148 . We also determine the covering radii of some extremal doubly even self-dual codes of length 80.

      PubDate: 2017-09-06T08:02:15Z
       
  • A complete characterization of Galois subfields of the generalized
           Giulietti–Korchmáros function field
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Nurdagül Anbar, Alp Bassa, Peter Beelen
      We give a complete characterization of all Galois subfields of the generalized Giulietti–Korchmáros function fields C n / F q 2 n for n ≥ 5 . Calculating the genera of the corresponding fixed fields, we find new additions to the list of known genera of maximal function fields.

      PubDate: 2017-09-06T08:02:15Z
       
  • Exact evaluation of second moments associated with some families of curves
           over a finite field
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Ravi Donepudi, Junxian Li, Alexandru Zaharescu
      Let F q be the finite field with q elements. Given an N-tuple Q ∈ F q N , we associate with it an affine plane curve C Q over F q . We consider the distribution of the quantity q − # C q , Q where # C q , Q denotes the number of F q -points of the affine curve C Q , for families of curves parameterized by Q. Exact formulae for first and second moments are obtained in several cases when Q varies over a subset of F q N . Families of Fermat type curves, Hasse–Davenport curves and Artin–Schreier curves are also considered and results are obtained when Q varies along a straight line.

      PubDate: 2017-09-06T08:02:15Z
       
  • A construction of q-ary linear codes with two weights
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Ziling Heng, Qin Yue
      Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of q-ary linear codes from trace and norm functions over finite fields. The weight distributions of the linear codes are determined in some cases based on Gauss sums. It is interesting that our construction can produce optimal or almost optimal codes. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.

      PubDate: 2017-08-31T14:30:42Z
       
  • On the dimension of twisted centralizer codes
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Adel Alahmadi, S.P. Glasby, Cheryl E. Praeger
      Given a field F, a scalar λ ∈ F and a matrix A ∈ F n × n , the twisted centralizer code C F ( A , λ ) : = { B ∈ F n × n A B − λ B A = 0 } is a linear code of length n 2 over F. When A is cyclic and λ ≠ 0 we prove that dim ⁡ C F ( A , λ ) = deg ⁡ ( gcd ⁡ ( c A ( t ) , λ n c A ( λ − 1 t ) ) ) where c A ( t ) denotes the characteristic polynomial of A. We also show how C F ( A , λ ) decomposes, and we estimate the probability that C F ( A , λ ) is nonzero when F is finite. Finally, we prove dim ⁡ C F ( A , λ ) ⩽ n 2 / 2 for λ ∉ { 0 , 1 } and ‘almost all’ n × n matrices A over F.

      PubDate: 2017-08-31T14:30:42Z
       
  • An application of random plane slicing to counting Fq-points on
           hypersurfaces
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Kaloyan Slavov
      Let X be an absolutely irreducible hypersurface of degree d in A n , defined over a finite field F q . The Lang–Weil bound gives an interval that contains # X ( F q ) . We exhibit an explicit interval, which does not contain # X ( F q ) , and which overlaps with the Lang–Weil interval. In particular, we sharpen the best known nontrivial lower bound for # X ( F q ) . The proof uses a combinatorial probabilistic technique.

      PubDate: 2017-08-31T14:30:42Z
       
  • The k-resultant modulus set problem on algebraic varieties over finite
           fields
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): David Covert, Doowon Koh, Youngjin Pi
      We study the k-resultant modulus set problem in the d-dimensional vector space F q d over the finite field F q with q elements. Given E ⊂ F q d and an integer k ≥ 2 , the k-resultant modulus set, denoted by Δ k ( E ) , is defined as Δ k ( E ) = { ‖ x 1 ± x 2 ± ⋯ ± x k ‖ ∈ F q : x j ∈ E ,   j = 1 , 2 , … , k } , where ‖ α ‖ = α 1 2 + ⋯ + α d 2 for α = ( α 1 , … , α d ) ∈ F q d . In this setting, the k-resultant modulus set problem is to determine the minimal cardinality of E ⊂ F q d such that Δ k ( E ) = F q or F q ⁎ . This problem is an extension of the Erdős–Falconer distance problem. In particular, we investigate the k-resultant modulus set problem with the restriction that the set E ⊂ F q d is contained in a specific algebraic variety. Energy estimates play a crucial role in our proof.

      PubDate: 2017-08-31T14:30:42Z
       
  • Number of rational branches of a singular plane curve over a finite field
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Nazar Arakelian
      Let F be a plane singular curve defined over a finite field F q . Via results of [11] and [1], the linear system of plane curves of a given degree passing through the singularities of F provides potentially good bounds for the number of points on a non-singular model of F . In this note, the case of a curve with two singularities such that the sum of their multiplicities is precisely the degree of the curve is investigated in more depth. In particular, such plane models are completely characterized, and for p > 3 , a curve of this type attaining one of the obtained bounds is presented.

      PubDate: 2017-08-31T14:30:42Z
       
  • Hypersurfaces achieving the Homma–Kim bound
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Andrea Luigi Tironi
      Let X n be a hypersurface in P n + 1 with n ≥ 2 defined over a finite field. The main result of this note is the classification, up to projective equivalence, of hypersurfaces X n without a linear component when the number of their rational points achieves the Homma–Kim bound.

      PubDate: 2017-08-31T14:30:42Z
       
  • A note on the differential spectrum of a differentially 4-uniform power
           function
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Maosheng Xiong, Haode Yan
      Let F ( x ) = x 2 2 k + 2 k + 1 be a power function over the finite field GF ( 2 n ) , where k is a positive integer and n = 4 k . It is known by a recent result of Bracken and Leander that F ( x ) is a highly nonlinear differentially 4-uniform function. Building upon this work, in this paper we determine the differential spectrum of F ( x ) .

      PubDate: 2017-08-31T14:30:42Z
       
  • Determinants of matrices over commutative finite principal ideal rings
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Parinyawat Choosuwan, Somphong Jitman, Patanee Udomkavanich
      In this paper, the determinants of n × n matrices over commutative finite chain rings and over commutative finite principal ideal rings are studied. The number of n × n matrices over a commutative finite chain ring R of a fixed determinant a is determined for all a ∈ R and positive integers n. Using the fact that every commutative finite principal ideal ring is a product of commutative finite chain rings, the number of n × n matrices of a fixed determinant over a commutative finite principal ideal ring is shown to be multiplicative, and hence, it can be determined. These results generalize the case of matrices over the ring of integers modulo m.

      PubDate: 2017-08-31T14:30:42Z
       
  • On the fixed points of the map x↦xx modulo a prime, II
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Adam Tyler Felix, Pär Kurlberg
      We study number theoretic properties of the map x ↦ x x ( mod p ) , where x ∈ { 1 , 2 , … , p − 1 } , and improve on some recent upper bounds, due to Kurlberg, Luca, and Shparlinski, on the number of primes p < N for which the map only has the trivial fixed point x = 1 . A key technical result, possibly of independent interest, is the existence of subsets N q ⊂ { 2 , 3 , … , q − 1 } such that almost all k-tuples of distinct integers n 1 , n 2 , … , n k ∈ N q are multiplicatively independent (if k is not too large), and N q = q ⋅ ( 1 + o ( 1 ) ) as q → ∞ . For q a large prime, this is used to show that the number of solutions to a certain large and sparse system of F q -linear forms { L n } n = 2 q − 1 “behaves randomly” in the sense that { v ∈ F q d : L n ( v ) = 1 , n = 2 , 3 , … , q − 1 } ∼ q d ( 1 − 1 / q ) q ∼ q d / e . (Here d = π ( q − 1 ) and the coefficients of L n are given by the exponents in the prime power factorisation of n.)

      PubDate: 2017-08-31T14:30:42Z
       
  • An extended characterization of a class of optimal three-weight cyclic
           codes over any finite field
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Gerardo Vega
      A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Almost immediately thereafter, several classes of cyclic codes with either optimal three weights or a few weights, were given in [3], showing at the same time that one of these classes can be constructed as a generalization of the sufficient numerical conditions of the characterization given in [10]. The main purpose of this work is to show that these numerical conditions that were found in [3], are also necessary. That is, the main contribution in this work is to present an extended characterization of a class of optimal three-weight cyclic codes, in terms of a weight distribution table. Now, note that the kind of characterizations that are given in terms of a weight distribution table are, in general, very difficult to establish. On the other hand, an interesting feature of the present work, in clear contrast with these two preceding works, is that we use some new and non-conventional methods in order to achieve our goals. In fact, through these non-conventional methods, we not only were able to extend the characterization in [10], but also present a less complex proof of such extended characterization, which avoids the use of some of the sophisticated – but at the same time complex – theorems, that are the key arguments of the proofs given in [10] and [3]. Furthermore, we also find the parameters for the dual code of any cyclic code in our extended characterization class. In fact, after the analysis of some examples, it seems that such dual codes always have the same parameters as the best known linear codes.

      PubDate: 2017-08-31T14:30:42Z
       
  • Some Ree and Suzuki curves are not Galois covered by the Hermitian curve
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Maria Montanucci, Giovanni Zini
      The Deligne–Lusztig curves associated to the algebraic groups of type A 2 2 , B 2 2 , and G 2 2 are classical examples of maximal curves over finite fields. The Hermitian curve H q is maximal over F q 2 , for any prime power q, the Suzuki curve S q is maximal over F q 4 , for q = 2 2 h + 1 , h ≥ 1 , and the Ree curve R q is maximal over F q 6 , for q = 3 2 h + 1 , h ≥ 0 . In this paper we show that S 8 is not Galois covered by H 64 . We also prove an unpublished result due to Rains and Zieve stating that R 3 is not Galois covered by H 27 . Furthermore, we determine the spectrum of genera of Galois subcovers of H 27 , and we point out that some Galois subcovers of R 3 are not Galois subcovers of H 27 .

      PubDate: 2017-08-31T14:30:42Z
       
  • A construction of linear codes and their complete weight enumerators
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Shudi Yang, Xiangli Kong, Chunming Tang
      Recently, linear codes constructed from defining sets have been studied extensively. They may have excellent parameters if the defining set is chosen properly. Let m > 2 be a positive integer. For an odd prime p, let r = p m and Tr be the absolute trace function from F r onto F p . In this paper, we give a construction of linear codes by defining the code C D = { ( Tr ( a x ) ) x ∈ D : a ∈ F r } , where D = { x ∈ F r : Tr ( x ) = 1 , Tr ( x 2 ) = 0 } . Its complete weight enumerator and weight enumerator are determined explicitly by employing cyclotomic numbers and Gauss sums. However, we find that the code is optimal with respect to the Griesmer bound provided that m = 3 . In fact, it is MDS when m = 3 . Moreover, the codes presented have higher rate compared with other codes, which enables them to have essential applications in areas such as association schemes and secret sharing schemes.

      PubDate: 2017-08-31T14:30:42Z
       
  • Algebraic Cayley graphs over finite local rings
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Arnisa Rasri, Yotsanan Meemark
      In this work, we define and study the algebraic Cayley directed graph over a finite local ring. Its vertex set is the unit group of a finite extension of a finite local ring R and its adjacency condition is that the quotient is a monic primary polynomial. We investigate its connectedness and diameter bound, and we also show that our graph is an expander graph. In addition, if a local ring has nilpotency two, then we obtain a better view of our graph from the lifting of the graph over its residue field.

      PubDate: 2017-08-31T14:30:42Z
       
  • On the structure of Z2Z2[u3]-linear and cyclic codes
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Ismail Aydogdu, Irfan Siap, Roger Ten-Valls
      Recently some special type of mixed alphabet codes that generalize the standard codes has attracted much attention. Besides Z 2 Z 4 -additive codes, Z 2 Z 2 [ u ] -linear codes are introduced as a new member of such families. In this paper, we are interested in a new family of such mixed alphabet codes, i.e., codes over Z 2 Z 2 [ u 3 ] where Z 2 [ u 3 ] = { 0 , 1 , u , 1 + u , u 2 , 1 + u 2 , u + u 2 , 1 + u + u 2 } is an 8-element ring with u 3 = 0 . We study and determine the algebraic structures of linear and cyclic codes defined over this family. First, we introduce Z 2 Z 2 [ u 3 ] -linear codes and give standard forms of generator and parity-check matrices and later we present generators of both cyclic codes and their duals over Z 2 Z 2 [ u 3 ] . Further, we present some examples of optimal binary codes which are obtained through Gray images of Z 2 Z 2 [ u 3 ] -cyclic codes.

      PubDate: 2017-08-31T14:30:42Z
       
  • A note on permutation polynomials over finite fields
    • Abstract: Publication date: November 2017
      Source:Finite Fields and Their Applications, Volume 48
      Author(s): Jingxue Ma, Gennian Ge
      Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are settled. Moreover, a new class of permutation trinomials of the form x + γ Tr q n / q ( x k ) is also presented, which generalizes two examples of [10].

      PubDate: 2017-08-31T14:30:42Z
       
  • 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
       
  • 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
       
  • 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
       
 
 
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