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MATHEMATICS (706 journals)                  1 2 3 4 | Last

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

        1 2 3 4 | Last

Journal Cover Cryptography and Communications
  [SJR: 0.55]   [H-I: 8]   [12 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447
   Published by Springer-Verlag Homepage  [2351 journals]
  • Enumeration formulae for self-dual, self-orthogonal and complementary-dual
           quasi-cyclic codes over finite fields
    • Authors: Anuradha Sharma; Taranjot Kaur
      Pages: 401 - 435
      Abstract: Let \(\mathbb {F}_{q}\) denote the finite field of order q, and let ℓ,m be positive integers with \(\gcd (m,q)=1.\) In this paper, we enumerate all self-orthogonal, self-dual and complementary-dual ℓ-quasi-cyclic codes of length m ℓ over \(\mathbb {F}_{q}\) by placing the Euclidean inner product on \(\mathbb {F}_{q}^{m\ell }.\)
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0228-7
      Issue No: Vol. 10, No. 3 (2018)
  • Two classes of near-optimal frequency-hopping sequence sets with
           prime-power period
    • Authors: Shanding Xu; Xiwang Cao; Guangkui Xu; Gaojun Luo
      Pages: 437 - 454
      Abstract: In this paper, a kind of generalized cyclotomy with respect to a prime power is introduced and properties of the corresponding generalized cyclotomic numbers are investigated. Based on the generalized cyclotomy, two classes of frequency-hopping sequence (FHS) sets with prime-power period are presented. Meanwhile, we derive the Hamming correlation distribution of the new FHS sets. The results show that the proposed FHSs and FHS sets have (near-) optimal maximum Hamming correlation (MHC). These classes of near-optimal FHS sets have new parameters which are not covered in the literature.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0229-6
      Issue No: Vol. 10, No. 3 (2018)
  • On lattice-based algebraic feedback shift registers synthesis for
    • Authors: Li-Ping Wang; Daqing Wan
      Pages: 455 - 465
      Abstract: In this paper we show that algebraic feedback shift registers synthesis problems over residue class rings, some ramified extensions and some quadratic integer rings for multisequences are reduced to the successive minima problem in lattice theory. Therefore they can be solved by polynomial-time algorithms since the number of multiple sequences is fixed.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0230-0
      Issue No: Vol. 10, No. 3 (2018)
  • The exact autocorrelation distribution and 2-adic complexity of a class of
           binary sequences with almost optimal autocorrelation
    • Authors: Yuhua Sun; Qiang Wang; Tongjiang Yan
      Pages: 467 - 477
      Abstract: Pseudo-random sequences with good statistical properties, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of binary sequences with three-level autocorrelation and analyze the 2-adic complexity of this class of sequences. Our results show that the 2-adic complexity of such a binary sequence with period N is at least (N + 1) − log2 (N + 1). We further show that it is maximal for infinitely many cases. This indicates that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0233-x
      Issue No: Vol. 10, No. 3 (2018)
  • Revisiting RC4 key collision: Faster search algorithm and new 22-byte
           colliding key pairs
    • Authors: Amit Jana; Goutam Paul
      Pages: 479 - 508
      Abstract: If two different secret keys of stream cipher RC4 yield the same internal state after the key scheduling algorithm (KSA) and hence generate the same sequence of keystream bits, they are called a colliding key pair. The number of possible internal states of RC4 stream cipher is very large (approximately 21700), which makes finding key collision hard for practical key lengths (i.e., less than 30 bytes). Matsui (2009) for the first time reported a 24-byte colliding key pair and one 20-byte near-colliding key pair (i.e., for which the state arrays after the KSA differ in at most two positions) for RC4. Subsequently, Chen and Miyaji (2011) designed a more efficient search algorithm using Matsui’s collision pattern and reported a 22-byte colliding key pair which remains the only shortest known colliding key pair so far. In this paper, we show some limitations of both the above approaches and propose a faster collision search algorithm that overcomes these limitations. Using our algorithm, we are able to find three additional 22-byte colliding key pairs that are different from the one reported by Chen and Miyaji. We additionally give 12 new 20-byte near-colliding key pairs. These results are significant, considering the argument by Biham and Dunkelman (2007), that for shorter keys there might be no instances of collision at all.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0231-z
      Issue No: Vol. 10, No. 3 (2018)
  • Generalized nonbinary sequences with perfect autocorrelation, flexible
           alphabets and new periods
    • Authors: Serdar Boztaş; Ferruh Özbudak; Eda Tekin
      Pages: 509 - 517
      Abstract: We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztaş and Udaya 10) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel alternatives for wireless communications and radar system designers for applications in ranging and synchronisation as well as channel identification.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0237-6
      Issue No: Vol. 10, No. 3 (2018)
  • Cyclic codes over a non-commutative finite chain ring
    • Authors: R. Sobhani
      Pages: 519 - 530
      Abstract: In this study, we consider the finite (not necessary commutative) chain ring \(\mathcal {R}:=\mathbb {F}_{p^{m}}[u,\theta ]/{\left < u^{2} \right >}\) , where θ is an automorphism of \(\mathbb {F}_{p^{m}}\) , and completely explore the structure of left and right cyclic codes of any length N over \(\mathcal {R}\) , that is, left and right ideals of the ring \(\mathcal {S}:=\mathcal {R}[x]/{\left < x^{N}-1 \right >}\) . For a left (right) cyclic code, we determine the structure of its right (left) dual. Using the fact that self-dual codes are bimodules, we discuss on self-dual cyclic codes over \(\mathcal {R}\) . Finally, we study Gray images of cyclic codes over \(\mathcal {R}\) and as some examples, three linear codes over \(\mathbb {F}_{4}\) with the parameters of the best known ones, but with different weight distributions, are obtained as the Gray images of cyclic codes over \(\mathcal {R}\) .
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0238-5
      Issue No: Vol. 10, No. 3 (2018)
  • Permutation polynomials of the form cx + Tr q l / q ( x a ) $cx+\text
           {Tr}_{q^{l}/ q}(x^{a})$ and permutation trinomials over finite fields with
           even characteristic
    • Authors: Kangquan Li; Longjiang Qu; Xi Chen; Chao Li
      Pages: 531 - 554
      Abstract: Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. Particularly, permutation polynomials with few terms are more popular for their simple algebraic form and additional extraordinary properties. Very recently, G. Kyureghyan and M.E. Zieve (2016) studied permutation polynomials over \(\mathbb {F}_{q^{n}}\) of the form \(x+\gamma \text {Tr}_{q^{n}/q}(x^{k})\) , where q is odd, and nine classes of permutation polynomials were constructed. In this paper, we present fifteen new classes of permutation polynomials of the form \(cx+\text {Tr}_{q^{l}/ q}(x^{a})\) over finite fields with even characteristic, which explain most of the examples with q = 2 k , k > 1, k l < 14 and \(c\in \mathbb {F}_{q^{l}}^{*}\) . Furthermore, we also construct four classes of permutation trinomials.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0236-7
      Issue No: Vol. 10, No. 3 (2018)
  • Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable
           codes with length 3
    • Authors: Xuli Zhang; Jing Jiang; Minquan Cheng
      Pages: 555 - 565
      Abstract: Separable code (SC, Cheng and Miao IEEE Trans. Inf. Theory 57, 4843–4851, 2011), frameproof code (FPC, Boneh and Shaw IEEE Trans. Inf. Theory 44, 1897–1905, 1998) and strongly separable code (SSC, Jiang et al. Des. Codes Cryptogr. 79:303–318, 2016) are used to construct anti-collusion codes. SSC is better than FPC and SC in the applications for multimedia fingerprinting since SSC has lower identifying complexity than that of SC (the same complexity as FPC) and weaker structure than that of FPC. In this paper, we first derive several upper bounds on the number of codewords of a \(\overline {t}\) -SSC. Then we focus on \(\overline {3}\) -SSCs with codeword length 3 and obtain the following two main results: (1) An equivalence between an SSC and an SC is derived; (2) An improved lower bound Ω(q 5/3 + q 4/3 − q) on the size of a q-ary SSC when \(q={q_{1}^{6}}\) for any prime power q 1 ≡ 1 (mod 6), which is better than the previously known bound \(\lfloor \sqrt {q}\rfloor ^{3}\) , is obtained by means of a difference matrix and a known result on the subsets of \(\mathbb {F}^{n}_{q}\) containing no three points on a line.
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0235-8
      Issue No: Vol. 10, No. 3 (2018)
  • New results on permutation polynomials of the form ( x p m − x + δ ) s
           + x p m + x over 𝔽 p 2m
    • Authors: Zhengbang Zha; Lei Hu; Zhizheng Zhang
      Pages: 567 - 578
      Abstract: Permutation polynomials over finite fields have significant applications in coding theory, cryptography, combinatorial designs and many other areas of mathematics and engineering. In this paper, we study the permutation behavior of polynomials with the form \((x^{p^{m}}-x+\delta )^{s}+x^{p^{m}}+x\) over the finite field \(\mathbb {F}_{p^{2m}}\) . By using the Akbary-Ghioca-Wang (AGW) criterion, we present several new classes of permutations over \(\mathbb {F}_{p^{2m}}\) based on some bijections over the set \(\{t\in \mathbb {F}_{p^{2m}} t^{p^{m}}+t=0\}\) or the subfield \(\mathbb {F}_{p^{m}}\) .
      PubDate: 2018-05-01
      DOI: 10.1007/s12095-017-0234-9
      Issue No: Vol. 10, No. 3 (2018)
  • Modified planar functions and their components
    • Authors: Nurdagül Anbar; Wilfried Meidl
      Pages: 235 - 249
      Abstract: Zhou (J. Combin. Des. 21(12), 563–584, 2013) introduced modified planar functions in order to describe (2 n , 2 n , 2 n , 1) relative difference sets R as a graph of a function on the finite field \(\mathbb {F}_{2^{n}}\) , and pointed out that projections of R are difference sets that can be described by negabent or bent4 functions, which are Boolean functions given in multivariate form. One of the objectives of this paper is to contribute to the understanding of these component functions of modified planar functions. We identify the versions of the Walsh transforms that apply to modified planar functions on \(\mathbb {F}_{2^{n}}\) and their components, obtain a description of modified planar functions by their components which is similar to that of the classical planar functions in odd characteristic as a vectorial bent function, and point out some further properties of these components. Finally we introduce vectorial bent4 functions (over finite fields), which correspond to relative difference sets in certain groups. We give conditions under which Maiorana-McFarland functions are such functions, hence give rise to relative difference sets in \(\mathbb {Z}_{2}^{n/2}\times \mathbb {Z}_{4}^{n/2}\) .
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0218-9
      Issue No: Vol. 10, No. 2 (2018)
  • Construction of de Bruijn sequences from product of two irreducible
    • Authors: Zuling Chang; Martianus Frederic Ezerman; San Ling; Huaxiong Wang
      Pages: 251 - 275
      Abstract: We study a class of Linear Feedback Shift Registers (LFSRs) with characteristic polynomial f(x) = p(x)q(x) where p(x) and q(x) are distinct irreducible polynomials in 𝔽2[x]. Important properties of the LFSRs, such as the cycle structure and the adjacency graph, are derived. A method to determine a state belonging to each cycle and a generic algorithm to find all conjugate pairs shared by any pair of cycles are given. The process explicitly determines the edges and their labels in the adjacency graph. The results are then combined with the cycle joining method to efficiently construct a new class of de Bruijn sequences. An estimate of the number of resulting sequences is given. In some cases, using cyclotomic numbers, we can determine the number exactly.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0219-8
      Issue No: Vol. 10, No. 2 (2018)
  • Classification and Construction of quaternary self-dual bent functions
    • Authors: Lin Sok; MinJia Shi; Patrick Solé
      Pages: 277 - 289
      Abstract: Quaternary self-dual bent functions are studied from the viewpoints of existence, construction, and symmetry. A search algorithm is described to classify their orbits under the orthogonal group in low dimensions. A connection with self-dual bent Boolean functions shows that they do not exist in odd number of variables.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0216-y
      Issue No: Vol. 10, No. 2 (2018)
  • The weight distribution of a class of two-weight linear codes derived from
           Kloosterman sums
    • Authors: Pan Tan; Zhengchun Zhou; Deng Tang; Tor Helleseth
      Pages: 291 - 299
      Abstract: Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, a class of p-ary two-weight linear codes is constructed using a generic construction developed by Ding et al. recently, where p is a prime. Their length and weight distribution are closed-form expressions of Kloosterman sums over prime finite fields, and are completely determined when p = 2 and p = 3. The dual of this class of linear codes is also studied and is shown to be optimal or almost optimal in the binary case.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0221-1
      Issue No: Vol. 10, No. 2 (2018)
  • Binary linear codes with two or three weights from niho exponents
    • Authors: Gaojun Luo; Xiwang Cao; Shanding Xu; Jiafu Mi
      Pages: 301 - 318
      Abstract: Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, date storage systems, strongly regular graphs and some other fields. In this paper, we present several classes of binary linear codes with two or three weights and study their weight distributions. Two classes of strongly regular graphs are constructed from binary linear codes with two weights. Numerical results show that some of the obtained codes are either optimal or near optimal with respect to certain bounds on linear codes.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0220-2
      Issue No: Vol. 10, No. 2 (2018)
  • A sequence construction of cyclic codes over finite fields
    • Authors: Cunsheng Ding
      Pages: 319 - 341
      Abstract: Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer electronics, and data storage systems. There are several approaches to constructing all cyclic codes over finite fields, including the generator matrix approach, the generator polynomial approach, and the generating idempotent approach. Another one is a sequence approach, which has been intensively investigated in the past decade. The objective of this paper is to survey the progress in this direction in the past decade. Many open problems are also presented in this paper.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0222-0
      Issue No: Vol. 10, No. 2 (2018)
  • Quadratic residue codes over the ring 𝔽 p [ u ] / 〈 u m − u
           〉 $\mathbb {F}_{p}[u]/\langle u^{m}-u\rangle $ and their Gray images
    • Authors: Mokshi Goyal; Madhu Raka
      Pages: 343 - 355
      Abstract: Let m ≥ 2 be any natural number and let \(\mathcal {R}=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^{2}\mathbb {F}_{p}+\cdots +u^{m-1}\mathbb {F}_{p}\) be a finite non-chain ring, where u m = u and p is a prime congruent to 1 modulo (m − 1). In this paper we study quadratic residue codes over the ring \(\mathcal {R}\) and their extensions. A Gray map from \(\mathcal {R}^{n}\) to \((\mathbb {F}_{p}^{m})^{n}\) is defined which preserves self duality of linear codes. As a consequence, we construct self-dual, formally self-dual and self-orthogonal codes over \(\mathbb {F}_{p}\) . To illustrate this, several examples of self-dual, self-orthogonal and formally self-dual codes are given. Among others a [9,3,6] linear code over \(\mathbb {F}_{7}\) is constructed which is self-orthogonal as well as nearly MDS. The best known linear code with these parameters (ref. Magma) is not self-orthogonal.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0223-z
      Issue No: Vol. 10, No. 2 (2018)
  • Perfect sequences over the quaternions and (4 n , 2, 4 n , 2 n )-relative
           difference sets in C n × Q 8
    • Authors: Santiago Barrera Acevedo; Heiko Dietrich
      Pages: 357 - 368
      Abstract: Perfect sequences over general quaternions were introduced in 2009 by Kuznetsov. The existence of perfect sequences of increasing lengths over the basic quaternions Q 8 = {±1, ±i, ±j, ±k} was established in 2012 by Barrera Acevedo and Hall. The aim of this paper is to prove a 1–1 correspondence between perfect sequences of length n over Q 8 ∪ q Q 8 with q = (1 + i + j + k)/2, and (4n, 2, 4n, 2n)-relative difference sets in C n × Q 8 with forbidden subgroup C 2; here C m is a cyclic group of order m. We show that if n = p a + 1 for a prime p and integer a ≥ 0 with n ≡ 2 mod 4, then there exists a (4n, 2, 4n, 2n)-relative different set in C n × Q 8 with forbidden subgroup C 2. Lastly, we show that every perfect sequence of length n over Q 8 ∪ q Q 8 yields a Hadamard matrix of order 4n (and a quaternionic Hadamard matrix of order n over Q 8 ∪ q Q 8).
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0224-y
      Issue No: Vol. 10, No. 2 (2018)
  • Matrix parametrized shift registers
    • Authors: Andrew Klapper
      Pages: 369 - 382
      Abstract: High speed pseudorandom sequence generators have played roles in an array of applications in communications, cryptography, and computing. At the heart of many of these generators are shift registers of various types. Researchers have studied linear feedback shift registers (LFSRs), feedback with carry shift registers (FCSRs), and various generalizations such as ring FCSRS and algebraic feedback shift registers. The analysis of these sequence generators typically proceeds by defining an algebraic structure on the set of infinite output sequences, based on a choice of uniformizing parameter (e.g., power series for LFSRs, N-adic numbers for FCSRs). In this paper we introduce a new generalization of FCSRs in which the uniformizing parameter \(N\in \mathbb {Z}\) is replaced by a square matrix, T, resulting in what we call T-generators. We describe an algebraic structure, the T-adic numbers, and use it to study the periodicity of T-generators.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0226-9
      Issue No: Vol. 10, No. 2 (2018)
  • Message Authentication Based on Cryptographically Secure CRC without
           Polynomial Irreducibility Test
    • Authors: Elena Dubrova; Mats Näslund; Göran Selander; Fredrik Lindqvist
      Pages: 383 - 399
      Abstract: In this paper, we present a message authentication scheme based on cryptographically secure cyclic redundancy check (CRC). Similarly to previously proposed cryptographically secure CRCs, the presented one detects both random and malicious errors without increasing bandwidth. The main difference from previous approaches is that we use random instead of irreducible generator polynomials. This eliminates the need for irreducibility tests. We provide a detailed quantitative analysis of the achieved security as a function of message and CRC sizes. The results show that the presented scheme is particularly suitable for the authentication of short messages.
      PubDate: 2018-03-01
      DOI: 10.1007/s12095-017-0227-8
      Issue No: Vol. 10, No. 2 (2018)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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