Subjects -> MATHEMATICS (Total: 1100 journals)
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MATHEMATICS (812 journals)                  1 2 3 4 5 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
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: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 40)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 11)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 8)
Advances in Mathematics     Full-text available via subscription   (Followers: 17)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in Numerical Analysis     Open Access   (Followers: 9)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 10)
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 9)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 3)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 8)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 12)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 5)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access   (Followers: 7)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 3)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
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  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 4)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 24)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 2)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
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: 3)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
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: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 1)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 22)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 3)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
ChemSusChem     Hybrid Journal   (Followers: 8)
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  
Ciencia     Open Access   (Followers: 1)
Clean Air Journal     Full-text available via subscription   (Followers: 1)
CODEE Journal     Open Access   (Followers: 3)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 15)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 4)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Discrete Mathematics     Open Access   (Followers: 2)
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access   (Followers: 2)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Cryptography and Communications
Journal Prestige (SJR): 0.446
Citation Impact (citeScore): 1
Number of Followers: 13  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447
Published by Springer-Verlag Homepage  [2626 journals]
  • Repeated-root constacyclic codes of length 2 p s over F p m + u F p m + u
           2 F p m $\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+u^{2}\mathbb
           {F}_{p^{m}}$
    • Abstract: Let λ be a unit of the finite commutative chain ring \(R=\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+u^{2}\mathbb {F}_{p^{m}}=\{\alpha +u\upbeta +u^{2}\gamma : \alpha ,\upbeta ,\gamma \in \mathbb { F}_{p^{m}}\}\) with u3 = 0, where p is an odd prime and m is a positive integer. In this paper, we consider any λ-constacyclic codes of length 2ps over R. In the case of square λ = δ2, where δ ∈ R, the algebraic structures of all λ-constacyclic codes of length 2ps over R are determined by the Chinese Remainder Theorem in terms of polynomial generators. Precisely, each λ-constacyclic code of length 2ps is represented as a direct sum of a (−δ)-constacyclic code and a δ-constacyclic code of length ps. In the case of non-square λ = α + uβ + u2γ or λ = α + uβ, where \(\alpha ,\upbeta ,\gamma \in \mathbb {F}_{p^{m}}\setminus \{0\}\) , it is shown that the ring \(\mathcal {R}=\frac {R[x]}{\langle x^{2p^{s}}-\lambda \rangle }\) is a chain ring. In the case of non-square \(\lambda =\alpha \in \mathbb {F}_{p^{m}}\setminus \{0\}\) , it turns out that λ-constacyclic codes are classified into 8 distinct types of ideals, and the detailed structures of ideals in each type are provided.
      PubDate: 2020-08-09
       
  • Computing the 2-adic complexity of two classes of Ding-Helleseth
           generalized cyclotomic sequences of periods of twin prime products
    • Abstract: This paper contributes to compute the 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences. Results show that the 2-adic complexity of these sequences is good enough to resist the attack by the rational approximation algorithm.
      PubDate: 2020-08-07
       
  • On Euclidean Hulls of MDS Codes
    • Abstract: In this paper, we propose a mechanism for the construction of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon (GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.
      PubDate: 2020-07-28
       
  • On decoding additive generalized twisted Gabidulin codes
    • Abstract: In this paper, we consider an interpolation-based decoding algorithm for a large family of maximum rank distance codes, known as the additive generalized twisted Gabidulin codes, over the finite field \(\mathbb {F}_{q^{n}}\) for any prime power q. This paper extends the work of the conference paper Li and Kadir (2019) presented at the International Workshop on Coding and Cryptography 2019, which decoded these codes over finite fields in characteristic two.
      PubDate: 2020-07-23
       
  • Permutation polynomials and factorization
    • Abstract: We discuss a special class of permutation polynomials over finite fields focusing on some recent work on their factorization. In particular we obtain permutation polynomials with various factorization patterns that are favoured for applications. We also address a wide range of problems of current interest concerning irreducible factors of the terms of sequences and iterations of such permutation polynomials.
      PubDate: 2020-07-22
       
  • Boolean functions with multiplicative complexity 3 and 4
    • Abstract: Multiplicative complexity (MC) is defined as the minimum number of AND gates required to implement a function with a circuit over the basis (AND, XOR, NOT). Boolean functions with MC 1 and 2 have been characterized in Fisher and Peralta (2002), and Find et al. (IJICoT 4(4), 222–236, 2017), respectively. In this work, we identify the affine equivalence classes for functions with MC 3 and 4. In order to achieve this, we utilize the notion of the dimension dim(f) of a Boolean function in relation to its linearity dimension, and provide a new lower bound suggesting that the multiplicative complexity of f is at least ⌈dim(f)/2⌉. For MC 3, this implies that there are no equivalence classes other than those 24 identified in Çalık et al. (2018). Using the techniques from Çalık et al. and the new relation between the dimension and MC, we identify all 1277 equivalence classes having MC 4. We also provide a closed formula for the number of n-variable functions with MC 3 and 4. These results allow us to construct AND-optimal circuits for Boolean functions that have MC 4 or less, independent of the number of variables they are defined on.
      PubDate: 2020-07-18
       
  • Two constructions of asymptotically optimal codebooks via the trace
           functions
    • Abstract: In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determin the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the Welch bound. Moreover, in the first construction, we generalize the result in Zhang and Feng (IEEE Trans. Inform. Theory 58(4), 2507–2511, 2012). In the second construction, we generalize the results in Hong et al. (IEEE Trans. Inf. Theory 60(6), 3698–3705, 2014), we can asymptotically achieve Welch bound for any odd prime p, we also derive the whole distribution of their inner products. The parameters of these codebooks are new.
      PubDate: 2020-07-15
       
  • Vectorial bent functions in odd characteristic and their components
    • Abstract: Bent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent function always has a bent dual, a non-weakly regular bent function can be either dual-bent or non-dual-bent. The classical constructions (like quadratic bent functions, Maiorana-McFarland or partial spread) yield weakly regular bent functions, but meanwhile one knows constructions of infinite classes of non-weakly regular bent functions of both types, dual-bent and non-dual-bent. In this article we focus on vectorial bent functions in odd characteristic. We first show that most p-ary bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular bent functions can be components of a vectorial bent function. We present the first construction of vectorial bent functions of which the components are non-weakly regular but dual-bent, and the first construction of vectorial bent functions with non-dual-bent components.
      PubDate: 2020-07-15
       
  • Cryptographic properties of small bijective S-boxes with respect to
           modular addition
    • Abstract: We define affine equivalence of S-boxes with respect to modular addition, and explore its use in cryptanalysis. We have identified classes of small bijective S-boxes with respect to this new equivalence, and experimentally computed their properties.
      PubDate: 2020-07-10
       
  • Some new bounds on LCD codes over finite fields
    • Abstract: In this paper, we show that LCD codes are not equivalent to non-LCD codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD(n,2) over \(\mathbb {F}_{3}\) and \(\mathbb {F}_{4}\) , where LD(n,2) := max{d∣thereexsitsan [n,2, d] LCD \( code~ over~ \mathbb {F}_{q}\}\) . We study the bound of LCD codes over \(\mathbb {F}_{q}\) and generalize a conjecture proposed by Galvez et al. about the minimum distance of binary LCD codes.
      PubDate: 2020-07-01
       
  • On degree- d zero-sum sets of full rank
    • Abstract: A set \(S \subseteq {{\mathbb {F}}_{2}^{n}}\) is called degree-d zero-sum if the sum \({\sum }_{s \in S} f(s)\) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of degree at most n − d − 1. We prove some results on the existence of degree-d zero-sum sets of full rank, i.e., those that contain n linearly independent elements, and show relations to degree-1 annihilator spaces of Boolean functions and semi-orthogonal matrices. We are particularly interested in the smallest of such sets and prove bounds on the minimum number of elements in a degree-d zero-sum set of rank n. The motivation for studying those objects comes from the fact that degree-d zero-sum sets of full rank can be used to build linear mappings that preserve special kinds of nonlinear invariants, similar to those obtained from orthogonal matrices and exploited by Todo, Leander and Sasaki for breaking the block ciphers Midori, Scream and iScream.
      PubDate: 2020-07-01
       
  • New asymptotically optimal three-dimensional wave-length/space/time
           optical orthogonal codes for OCDMA systems
    • Abstract: We present new families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks. The families are based in the extended rational cycle used for the 2-D Moreno-Maric construction. The new families are asymptotically optimal with respect to the Johnson bound.
      PubDate: 2020-07-01
       
  • On the number of the rational zeros of linearized polynomials and the
           second-order nonlinearity of cubic Boolean functions
    • Abstract: Determine the number of the rational zeros of any given linearized polynomial is one of the vital problems in finite field theory, with applications in modern symmetric cryptosystems. But, the known general theory for this task is much far from giving the exact number when applied to a specific linearized polynomial. The first contribution of this paper is a better general method to get a more precise upper bound on the number of rational zeros of any given linearized polynomial over arbitrary finite field. We anticipate this method would be applied as a useful tool in many research branches of finite field and cryptography. Really we apply this result to get tighter estimations of the lower bounds on the second-order nonlinearities of general cubic Boolean functions, which has been an active research problem during the past decade. Furthermore, this paper shows that by studying the distribution of radicals of derivatives of a given Boolean function one can get a better lower bound of the second-order nonlinearity, through an example of the monomial Boolean functions \(g_{\mu }=Tr(\mu x^{2^{2r}+2^{r}+1})\) defined over the finite field \({\mathbb F}_{2^{n}}\) .
      PubDate: 2020-07-01
       
  • Solving x + x 2 l + ⋯ + x 2 m l = a $x+x^{2^{l}}+\cdots +x^{2^{ml}}=a$
           over F 2 n $\mathbb {F}_{2^{n}}$
    • Abstract: This paper presents an explicit representation for the solutions of the equation \({\sum }_{i=0}^{\frac kl-1}x^{2^{li}} = a \in \mathbb {F}_{2^{n}}\) for any given positive integers k, l with l k and n, in the closed field \({\overline {\mathbb {F}_{2}}}\) and in the finite field \(\mathbb {F}_{2^{n}}\) . As a by-product of our study, we are able to completely characterize the a’s for which this equation has solutions in \(\mathbb {F}_{2^{n}}\) .
      PubDate: 2020-07-01
       
  • Almost supplementary difference sets and quaternary sequences with optimal
           autocorrelation
    • Abstract: We introduce almost supplementary difference sets (ASDS). For odd m, certain ASDS in \(\mathbb Z_{m}\) that have amicable incidence matrices are equivalent to quaternary sequences of odd length m with optimal autocorrelation. As one consequence, if 2m − 1 is a prime power, or m ≡ 1 mod 4 is prime, then ASDS of this kind exist. We also explore connections to optimal binary sequences and group cohomology.
      PubDate: 2020-07-01
       
  • Double bordered constructions of self-dual codes from group rings over
           Frobenius rings
    • Abstract: In this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings \(\mathbb {F}_{2}+u\mathbb {F}_{2}\) and \(\mathbb {F}_{4}+u\mathbb {F}_{4}\) . We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.
      PubDate: 2020-07-01
       
  • Notes on generalized Hamming weights of some classes of binary codes
    • Abstract: Some classes of binary codes constructed by using some defining sets are studied, and for most defining sets, we will determine the generalized Hamming weight of the corresponding codes completely, and for other defining sets, we will determine part of the generalized Hamming weight of the corresponding codes.
      PubDate: 2020-07-01
       
  • The 2-adic complexity of a class of binary sequences with optimal
           autocorrelation magnitude
    • Abstract: Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on Ding-Helleseth-Lam sequences and interleaving technique (Designs, Codes and Cryptography 86, 1329–1338, 2018). The linear complexity of this class of sequences has been proved to be large enough to resist the B-M Algorithm by Fan (Designs, Codes and Cryptography 86, 2441–2450, 2018). In this paper, we study the 2-adic complexities of these sequences with period 4p and show they are no less than 2p, i.e., its 2-adic complexity is large enough to resist the Rational Approximation Algorithm.
      PubDate: 2020-07-01
       
  • About the linear complexity of quaternary sequences with even length
    • Abstract: Several classes of quaternary sequences of even period with optimal autocorrelation have been constructed by Su et al. based on interleaving certain kinds of binary sequences of odd period, i.e. Legendre sequence, twin-prime sequence and generalized GMW sequence. In this correspondence, the exact values of linear complexity over finite field \(\mathbb {F}_{4}\) and Galois ring \(\mathbb {Z}_{4}\) of the quaternary sequences are derived, respectively.
      PubDate: 2020-07-01
       
  • The minimum distance of new generalisations of the punctured binary
           Reed-Muller codes
    • Abstract: In 2018, Ding et al. introduced a new generalisation of the punctured binary Reed-Muller codes to construct LCD codes and 2-designs. They studied the minimum distance of the codes and proposed an open problem about the minimum distance. In this paper, several new results on the minimum distance of the generalised punctured binary Reed- Muller are presented. Particularly, some of the results are a generalisation or improvement of previous results in (Finite Fields Appl. 53, 144–174, 2018).
      PubDate: 2020-07-01
       
 
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