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  Subjects -> MATHEMATICS (Total: 912 journals)
    - APPLIED MATHEMATICS (76 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (678 journals)
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MATHEMATICS (678 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 6)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 11)
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: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 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: 9)
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 Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 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: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
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: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
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: 5)
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: 21)
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: 3)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 6)
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: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 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: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 7)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
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  
Current Research in Biostatistics     Open Access   (Followers: 10)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
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)

        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  [3120 journals]
  • Relative generalized Hamming weights of cyclic codes
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Jun Zhang, Keqin Feng
      Relative generalized Hamming weights (RGHWs) of a linear code with respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the linear codes. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems. In this paper, we investigate the RGHWs of cyclic codes of two nonzeros with respect to its irreducible cyclic subcodes. We give two formulae for RGHWs of the cyclic codes. As applications of the formulae, explicit examples are computed. Moreover, RGHWs of cyclic codes in the examples are very large, comparing with the generalized Plotkin bound of RGHWs. So it guarantees very high security for the secret sharing scheme based on the dual codes.

      PubDate: 2018-01-09T23:58:56Z
       
  • Preliminary results on the minimal polynomial of modified de Bruijn
           sequences
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Lin Tan, Hong Xu, Wen-Feng Qi
      Modified de Bruijn sequences are created by removing a single zero from the longest run of zeros of de Bruijn sequences. There are few theoretical results on the minimal polynomial and linear complexity of modified de Bruijn sequences. Some preliminary results are presented in this paper. It shows that for the minimal polynomial of a modified de Bruijn sequence of order n there exists at least one irreducible factor of degree n. An equivalent condition on which a polynomial is the minimal polynomial of some modified de Bruijn sequence is derived, using the tool of rational fraction representation of periodic sequences. Based on the equivalent condition, the impossible linear complexity of modified de Bruijn sequences can be discussed.

      PubDate: 2018-01-09T23:58:56Z
       
  • Geometrically nilpotent subvarieties
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Alexander Borisov
      We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several related open questions are stated and discussed.

      PubDate: 2018-01-09T23:58:56Z
       
  • The classification of antipodal two-weight linear codes
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Dieter Jungnickel, Vladimir D. Tonchev
      By a classical result of Bonisoli, the equidistant linear codes over GF ( q ) are, up to monomial equivalence, just the replications of some q-ary simplex code, possibly with added 0-coordinates. We prove an analogous result for the antipodal two-weight linear codes over GF ( q ) (that is, one of the two weights is the length of the code): up to monomial equivalence, any such code is ether a replication of a first order generalized Reed–Muller code, or a replication of a 3-dimensional projective code associated with some non-trivial maximal arc in the classical projective plane PG ( 2 , 2 s ) , s ≥ 1 . An equivalent geometric formulation of this result reads as follows: a multiset S of points spanning Π = PG ( m , q ) , m ≥ 2 , for which every hyperplane intersecting S does so in a constant number of points (counted with multiplicity), is either a multiple of a maximal arc in Π (for m = 2 ) or a multiple of the complement of some hyperplane of Π.

      PubDate: 2018-01-09T23:58:56Z
       
  • On the next-to-minimal weight of projective Reed–Muller codes
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Cícero Carvalho, Victor G.L. Neumann
      In this paper we present several values for the next-to-minimal weights of projective Reed–Muller codes. We work over F q with q ≥ 3 since in [3] we have determined the complete values for the next-to-minimal weights of binary projective Reed–Muller codes. As in [3] here we also find examples of codewords with next-to-minimal weight whose set of zeros is not in a hyperplane arrangement.

      PubDate: 2018-01-09T23:58:56Z
       
  • New 2-designs from strong difference families
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Simone Costa, Tao Feng, Xiaomiao Wang
      Strong difference families will be used to get: seven 2-designs whose parameter sets were previously in doubt; a strong indication about the existence of 2- ( p q , p , 1 ) designs with p ∈ { 13 , 17 } and q a prime power; a better asymptotic bound on prime powers q for which there exists an ( F p × F q , F p × { 0 } , k , λ ) relative difference family with p a prime power and k ∈ { p , p + 1 } .

      PubDate: 2018-01-09T23:58:56Z
       
  • Pure Weierstrass gaps from a quotient of the Hermitian curve
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Shudi Yang, Chuangqiang Hu
      In this paper, by employing some results on Kummer extensions, we give an arithmetic characterization of pure Weierstrass gaps at many totally ramified places on a quotient of the Hermitian curve, including the well-studied Hermitian curve as a special case. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results.

      PubDate: 2017-12-26T20:48:43Z
       
  • Normal bases and irreducible polynomials
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Hua Huang, Shanmeng Han, Wei Cao
      A normal basis of F q n over F q is a basis of the form { α , α q , … , α q n − 1 } . An irreducible polynomial in F q [ x ] is called an N-polynomial if its roots are linearly independent over F q . Let p be the characteristic of F q . Pelis et al. showed that every monic irreducible polynomial with degree n and nonzero trace is an N-polynomial provided that n is either a power of p or a prime different from p and q is a primitive root modulo n. Chang et al. proved that the converse is also true. By comparing the number of N-polynomials with that of irreducible polynomials with nonzero traces, we present an alternative treatment to this problem and show that all the results mentioned above can be easily deduced from our main theorem.

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

      PubDate: 2017-12-26T20:48:43Z
       
  • Some new non-additive maximum rank distance codes
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Kamil Otal, Ferruh Özbudak
      In this paper, a construction of maximum rank distance (MRD) codes as a generalization of generalized Gabidulin codes is given. The family of the resulting codes is not covered properly by additive generalized twisted Gabidulin codes, and does not cover all twisted Gabidulin codes. When the basis field has more than two elements, this family includes also non-affine MRD codes, and such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters.

      PubDate: 2017-12-26T20:48:43Z
       
  • New permutation quadrinomials over F22m
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ziran Tu, Xiangyong Zeng, Tor Helleseth
      In this paper, we propose a class of permutation polynomials over the finite field F 2 2 m for odd m. These permutations are generally quadrinomials, and some permutation trinomials can also be obtained.

      PubDate: 2017-12-26T20:48:43Z
       
  • On period polynomials of degree 2m and weight distributions of certain
           irreducible cyclic codes
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ioulia N. Baoulina
      We explicitly determine the values of reduced cyclotomic periods of order 2 m , m ≥ 4 , for finite fields of characteristic p ≡ 3  or  5 ( mod 8 ) . These evaluations are applied to obtain explicit factorizations of the corresponding reduced period polynomials. As another application, the weight distributions of certain irreducible cyclic codes are described.

      PubDate: 2017-12-26T20:48:43Z
       
  • All α+uβ-constacyclic codes of length nps over Fpm+uFpm
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Wei Zhao, Xilin Tang, Ze Gu
      Let F p m be a finite field with cardinality p m and R = F p m + u F p m with u 2 = 0 . We aim to determine all α + u β -constacyclic codes of length n p s over R, where α , β ∈ F p m ⁎ , n , s ∈ N + and gcd ⁡ ( n , p ) = 1 . Let α 0 ∈ F p m ⁎ and α 0 p s = α . The residue ring R [ x ] / 〈 x n p s − α − u β 〉 is a chain ring with the maximal ideal 〈 x n − α 0 〉 in the case that x n − α 0 is irreducible in F p m [ x ] . If x n − α 0 is reducible in F p m [ x ] , we give the explicit expressions of the ideals of R [ x ] / 〈 x n p s − α − u β 〉 . Besides, the number of codewords and the dual code of every α + u β -constacyclic code are provided.

      PubDate: 2017-12-13T06:22:49Z
       
  • Some new results on the self-dual [120,60,24] code
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Martino Borello, Javier de la Cruz
      The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further restrictions. Finally, we present some necessary conditions for the existence of the code, based on shadow and design theory.

      PubDate: 2017-12-13T06:22:49Z
       
  • The arithmetic of consecutive polynomial sequences over finite fields
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Domingo Gómez-Pérez, Alina Ostafe, Min Sha
      Motivated by a question of van der Poorten about the existence of an infinite chain of prime numbers (with respect to some base), in this paper we advance the study of sequences of consecutive polynomials whose coefficients are chosen consecutively from a sequence in a finite field of odd prime characteristic. We study the arithmetic of such sequences, including bounds for the largest degree of irreducible factors, the number of irreducible factors, as well as for the number of such sequences of fixed length in which all the polynomials are irreducible.

      PubDate: 2017-12-13T06:22:49Z
       
  • Hartmann–Tzeng bound and skew cyclic codes of designed Hamming
           distance
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): José Gómez-Torrecillas, F.J. Lobillo, Gabriel Navarro, Alessando Neri
      The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming distance is gained, and it is possible to design efficient decoding algorithms. In this paper, we give a version of the Hartmann–Tzeng bound that works for a wide class of skew cyclic codes. We also provide a practical method for constructing them with designed distance. For skew BCH codes, which are covered by our constructions, we discuss decoding algorithms. Detailed examples illustrate both the theory as the constructive methods it supports.

      PubDate: 2017-12-13T06:22:49Z
       
  • The octonions as a twisted group algebra
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Tathagata Basak
      We show that the octonions can be defined as the R -algebra with basis { e x : x ∈ F 8 } and multiplication given by e x e y = ( − 1 ) φ ( x , y ) e x + y , where φ ( x , y ) = tr ( y x 6 ) . While it is well known that the octonions can be described as a twisted group algebra, our purpose is to point out that this is a useful description. We show how the basic properties of the octonions follow easily from our definition. We give a uniform description of the sixteen orders of integral octonions containing the Gravesian integers, and a computation-free proof of their existence.

      PubDate: 2017-12-13T06:22:49Z
       
  • Repeated-root two-dimensional constacyclic codes of length 2ps.2k
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Zohreh Rajabi, Kazem Khashyarmanesh
      Let p be an odd prime. The main purpose of this paper is to establish and exploit the algebraic structure of some repeated-root two dimensional constacyclic codes of length 2 p s . 2 k over the finite field F p m . Moreover, we study all self-dual repeated-root two-dimensional ( λ , 1 ) -constacyclic codes of length 2 p s . 2 or 2 p s . 2 2 over F p m for λ ∈ { − 1 , 1 } .

      PubDate: 2017-12-13T06:22:49Z
       
  • Constructions of optimal LCD codes over large finite fields
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Lin Sok, Minjia Shi, Patrick Solé
      In this paper 1 , we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.

      PubDate: 2017-12-13T06:22:49Z
       
  • Kronecker–Halton sequences in Fp((X−1))
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Roswitha Hofer
      In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.

      PubDate: 2017-12-13T06:22:49Z
       
  • A class of new permutation trinomials
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Ziran Tu, Xiangyong Zeng, Chunlei Li, Tor Helleseth
      In this paper, we characterize the coefficients of f ( x ) = x + a 1 x q ( q − 1 ) + 1 + a 2 x 2 ( q − 1 ) + 1 in F q 2 [ x ] for even q that lead f ( x ) to be a permutation of F q 2 . We transform the problem into studying some low-degree equations with variable in the unit circle, which are intensively investigated with some parameterization techniques. From the numerical results, the coefficients that lead f ( x ) to be a permutation appear to be completely characterized in this paper. It is also demonstrated that some permutations proposed in this paper are quasi-multiplicative (QM) inequivalent to the previously known permutation trinomials.

      PubDate: 2017-12-13T06:22:49Z
       
  • Further results on permutation polynomials of the form
           (xpm−x+δ)s+x over Fp2m
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Rohit Gupta, R.K. Sharma
      Let F q denote the finite field of order q. In this paper, some new classes of permutation polynomials of the form ( x p m − x + δ ) s + x over F p 2 m are obtained by determining the number of solutions of certain equations.

      PubDate: 2017-12-13T06:22:49Z
       
  • Strongly regular Cayley graphs from partitions of subdifference sets of
           the Singer difference sets
    • Abstract: Publication date: March 2018
      Source:Finite Fields and Their Applications, Volume 50
      Author(s): Koji Momihara, Qing Xiang
      In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters.

      PubDate: 2017-12-13T06:22:49Z
       
  • Factoring polynomials of the form f(xn)∈Fq[x]
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): F.E. Brochero Martínez, Lucas Reis
      Let f ( x ) ∈ F q [ x ] be an irreducible polynomial of degree m and exponent e. For each positive integer n, such that ν p ( q − 1 ) ≥ ν p ( e ) + ν p ( n ) for all prime divisors p of n, we show a fast algorithm to determine the irreducible factors of f ( x n ) . Using this algorithm, we give the complete factorization of x n − 1 into irreducible factors in the case where n = d p t , p is an odd prime, q is a generator of the group Z p 2 ⁎ and either d = 2 m with m ≤ ν 2 ( q − 1 ) or d = r a , where r is a prime dividing q − 1 but not p − 1 .

      PubDate: 2017-12-13T06:22:49Z
       
  • Maximum distance separable codes for b-symbol read channels
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Baokun Ding, Tao Zhang, Gennian Ge
      Recently, Yaakobi et al. introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound for b-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum b-distance. We introduce a construction method using projective geometry, and then construct several infinite families of linear MDS b-symbol codes over finite fields. The lengths of these codes have a large range. And in some sense, we completely determine the existence of linear MDS b-symbol codes over finite fields for certain parameters.

      PubDate: 2017-12-13T06:22:49Z
       
  • Permutation polynomials over finite rings
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Dalma Görcsös, Gábor Horváth, Anett Mészáros
      Let PPol ( R ) denote the group of permutation polynomial functions over the finite, commutative, unital ring R under composition. We generalize numerous results about permutation polynomials over Z p n to local rings by treating them under a unified manner. In particular, we provide a natural wreath product decomposition of permutation polynomial functions over the maximal ideal M and over the finite field R / M . We characterize the group of permutation polynomial functions over M whenever the condition M R / M = { 0 } applies. Then we derive the size of PPol ( R ) , thereby generalizing the same size formulas for Z p n . Finally, we completely characterize when the group PPol ( R ) is solvable, nilpotent, or abelian.

      PubDate: 2017-12-13T06:22:49Z
       
  • Some permutation pentanomials over finite fields with even characteristic
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Guangkui Xu, Xiwang Cao, Jingshui Ping
      Six classes of permutation pentanomials are constructed from fractional polynomials which permute the set of ( 2 m + 1 ) -th roots of unity. Based on an approach which is a generalization of the work of Zha, Hu and Fan, some permutation pentanomials and trinomials are also obtained from known permutations of the set of ( 2 m + 1 ) -th roots of unity.

      PubDate: 2017-12-13T06:22:49Z
       
  • Galois LCD codes over finite fields
    • Abstract: Publication date: January 2018
      Source:Finite Fields and Their Applications, Volume 49
      Author(s): Xiusheng Liu, Yun Fan, Hualu Liu
      In this paper, we generalize the linear complementary dual codes (LCD codes for short) to k-Galois LCD codes, and study them by a uniform method. A necessary and sufficient condition for linear codes to be k-Galois LCD codes is obtained, two classes of k-Galois LCD MDS codes are exhibited. Then, necessary and sufficient conditions for λ-constacyclic codes being k-Galois LCD codes are characterized. Some classes of k-Galois LCD λ-constacyclic MDS codes are constructed. Finally, we study Hermitian LCD λ-constacyclic codes, and present a class of Hermitian LCD λ-constacyclic MDS codes.

      PubDate: 2017-12-13T06:22:49Z
       
  • 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
       
  • 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
       
  • 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
       
 
 
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