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  Subjects -> MATHEMATICS (Total: 864 journals)
    - APPLIED MATHEMATICS (69 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (642 journals)
    - MATHEMATICS (GENERAL) (40 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (75 journals)

MATHEMATICS (642 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: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
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: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 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: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
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: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Applicable Algebra in Engineering, Communication and Computing
  [SJR: 0.354]   [H-I: 27]   [2 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0622 - ISSN (Online) 0938-1279
   Published by Springer-Verlag Homepage  [2341 journals]
  • New algorithm for the elliptic curve discrete logarithm problem with
           auxiliary inputs
    • Authors: Jiang Weng; Yunqi Dou; Chuangui Ma
      Pages: 99 - 108
      Abstract: Abstract The discrete logarithm problem with auxiliary inputs (DLP-wAI) is a special discrete logarithm problem. Cheon first proposed a novel algorithm to solve the discrete logarithm problem with auxiliary inputs. Given a cyclic group \({\mathbb {G}}=\langle P\rangle \) of order p and some elements \(P,\alpha P,\alpha ^2 P,\ldots , \alpha ^d P\in {\mathbb {G}}\) , an attacker can recover \(\alpha \in {\mathbb {Z}}_p^*\) in the case of \(d (p\pm 1)\) with running time of \({\mathcal {O}}(\sqrt{(p\pm 1)/d}+d^i)\) group operations by using \({\mathcal {O}}(\text {max}\{\sqrt{(p\pm 1)/d}, \sqrt{d}\})\) storage ( \(i=\frac{1}{2}\) or 1 for \(d (p-1)\) case or \(d (p+1)\) case, respectively). In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs (ECDLP-wAI). We show that if some points \(P,\alpha P,\alpha ^k P,\alpha ^{k^2} P,\alpha ^{k^3} P,\ldots ,\alpha ^{k^{\varphi (d)-1}}P\in {\mathbb {G}}\) and multiplicative cyclic group \(K=\langle k \rangle \) are given, where d is a prime, \(\varphi (d)\) is the order of K and \(\varphi \) is the Euler totient function, the secret key \(\alpha \in {\mathbb {Z}}_p^*\) can be solved in \({\mathcal {O}}(\sqrt{(p-1)/d}+d)\) group operations by using \({\mathcal {O}}(\sqrt{(p-1)/d})\) storage.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0301-z
      Issue No: Vol. 28, No. 2 (2017)
       
  • A simple method for obtaining relations among factor basis elements for
           special hyperelliptic curves
    • Authors: Palash Sarkar; Shashank Singh
      Pages: 109 - 130
      Abstract: Abstract Nagao proposed a decomposition method for divisors of hyperelliptic curves defined over a field \({\mathbb {F}}_{q^n}\) with \(n\ge 2\) . Joux and Vitse later proposed a variant which provided relations among the factor basis elements. Both Nagao’s and the Joux–Vitse methods require solving a multi-variate system of polynomial equations. In this work, we revisit Nagao’s approach with the idea of avoiding the requirement of solving a multi-variate system. While this cannot be done in general, we are able to identify special cases for which this is indeed possible. Our main result is for curves \(C:y^2=f(x)\) of genus g defined over \({\mathbb {F}}_{q^2}\) having characteristic >2. If there is no restriction on f(x), we show that it is possible to obtain a relation in \((4g+4)!\) trials. The number of trials, though high, quantifies the computation effort needed to obtain a relation. This is in contrast to the methods of Nagao and Joux–Vitse which are based on solving systems of polynomial equations, for which the computation effort is hard to precisely quantify. The new method combines well with a sieving technique proposed by Joux and Vitse. If f(x) has a special form, then the number of trials can be significantly lower. For example, if f(x) has at most g consecutive coefficients which are in \({\mathbb {F}}_{q^2}\) while the rest are in \({\mathbb {F}}_q\) , then we show that it is possible to obtain a single relation in about \((2g+3)!\) trials. Our implementation of the resulting algorithm provides examples of factor basis relations for \(g=5\) and \(g=6\) . To the best of our knowledge, none of the previous methods known in the literature can provide such relations faster than our method. Other than obtaining such decompositions, we also explore the applicability of our approach for \(n>2\) and for binary characteristic fields.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0299-2
      Issue No: Vol. 28, No. 2 (2017)
       
  • Some classes of linear codes over $$\mathbb {Z}_4+v\mathbb {Z}_4$$ Z 4 + v
           Z 4 and their applications to construct good and new $$\mathbb {Z}_4$$ Z 4
           -linear codes
    • Authors: Jian Gao; Fang-Wei Fu; Yun Gao
      Pages: 131 - 153
      Abstract: Abstract Some classes of linear codes over the ring \(\mathbb {Z}_4+v\mathbb {Z}_4\) with \(v^2=v\) are considered. Construction of Euclidean formally self-dual codes and unimodular complex lattices from self-dual codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) are studied. Structural properties of cyclic codes and quadratic residue codes are also considered. Finally, some good and new \(\mathbb {Z}_4\) -linear codes are constructed from linear codes over \(\mathbb {Z}_4+v\mathbb {Z}_4\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0300-0
      Issue No: Vol. 28, No. 2 (2017)
       
  • Several classes of Boolean functions with few Walsh transform values
    • Authors: Guangkui Xu; Xiwang Cao; Shanding Xu
      Pages: 155 - 176
      Abstract: Abstract In this paper, several classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions. Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones.
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0298-3
      Issue No: Vol. 28, No. 2 (2017)
       
  • Minimal logarithmic signatures for one type of classical groups
    • Authors: Haibo Hong; Licheng Wang; Haseeb Ahmad; Jun Shao; Yixian Yang
      Pages: 177 - 192
      Abstract: Abstract As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like \(MST_1\) , \(MST_2\) and \(MST_3\) . An LS with the shortest length, called a minimal logarithmic signature (MLS), is even desirable for cryptographic applications. The MLS conjecture states that every finite simple group has an MLS. Recently, the conjecture has been shown to be true for general linear groups \(GL_n(q)\) , special linear groups \(SL_n(q)\) , and symplectic groups \(Sp_n(q)\) with q a power of primes and for orthogonal groups \(O_n(q)\) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group \(O_n(q)\) and \(SO_n(q)\) with q a power of an odd prime. Furthermore, we give constructions of MLSs for a type of classical groups—the projective commutator subgroup \(P{\varOmega }_n(q)\) .
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-016-0302-y
      Issue No: Vol. 28, No. 2 (2017)
       
  • Counting permutation equivalent degree six binary polynomials invariant
           under the cyclic group
    • Authors: Florian Luca; Pantelimon Stănică
      Pages: 1 - 10
      Abstract: Abstract In this paper we find an exact formula for the number of affine equivalence classes under permutations for binary polynomials degree \(d=6\) invariant under the cyclic group (also, called monomial rotation symmetric), for a prime number of variables; this extends previous work for \(2\le d\le 5\) .
      PubDate: 2017-01-01
      DOI: 10.1007/s00200-016-0294-7
      Issue No: Vol. 28, No. 1 (2017)
       
  • A construction of several classes of two-weight and three-weight linear
           codes
    • Authors: Chengju Li; Qin Yue; Fang-Wei Fu
      Pages: 11 - 30
      Abstract: Abstract Linear codes constructed from defining sets have been extensively studied and may have a few nonzero weights if the defining sets are well chosen. Let \({\mathbb {F}}_q\) be a finite field with \(q=p^m\) elements, where p is a prime and m is a positive integer. Motivated by Ding and Ding’s recent work (IEEE Trans Inf Theory 61(11):5835–5842, 2015), we construct p-ary linear codes \({\mathcal {C}}_D\) by $$\begin{aligned} {\mathcal {C}}_D=\{{\mathbf {c}}(a,b)=\big (\text {Tr}_m(ax+by)\big )_{(x,y)\in D}: a, b \in {\mathbb {F}}_q\}, \end{aligned}$$ where \(D \subset {\mathbb {F}}_q^2\) and \(\text {Tr}_m\) is the trace function from \({\mathbb {F}}_q\) onto \({\mathbb {F}}_p\) . In this paper, we will employ exponential sums to investigate the weight enumerators of the linear codes \({\mathcal {C}}_D\) , where \(D=\{(x, y) \in {\mathbb {F}}_q^2 \setminus \{(0,0)\}: \text {Tr}_m(x^{N_1}+y^{N_2})=0\}\) for two positive integers \(N_1\) and \(N_2\) . Several classes of two-weight and three-weight linear codes and their explicit weight enumerators are presented if \(N_1, N_2 \in \{1, 2, p^{\frac{m}{2}}+1\}\) . By deleting some coordinates, more punctured two-weight and three-weight linear codes \({\mathcal {C}}_{\overline{D}}\) which include some optimal codes are derived from \({\mathcal {C}}_D\) .
      PubDate: 2017-01-01
      DOI: 10.1007/s00200-016-0297-4
      Issue No: Vol. 28, No. 1 (2017)
       
  • On the annihilator ideal of an inverse form
    • Authors: Graham H. Norton
      Pages: 31 - 78
      Abstract: Abstract Let \(\mathbbm {k}\) be a field. We simplify and extend work of Althaler and Dür on finite sequences over \(\mathbbm {k}\) by regarding \(\mathbbm {k}[x^{-1},z^{-1}]\) as a \(\mathbbm {k}[x,z]\) module and studying forms in \(\mathbbm {k}[x^{-1},z^{-1}]\) from first principles. Then we apply our results to finite sequences. First we define the annihilator ideal \(\mathcal {I}_F\) of a form \(F\in \mathbbm {k}[x^{-1},z^{-1}]\) of total degree \(m\le 0\) . This is a homogeneous ideal. We inductively construct an ordered pair ( \(f_1\) ,  \(f_2\) ) of forms in \(\mathbbm {k}[x,z]\) which generate \(\mathcal {I}_F\)  ; our generators are special in that z does not divide the leading grlex monomial of \(f_1\) but z divides \(f_2\) , and the sum of their total degrees is always \(2-m\) . The corresponding algorithm is \(\sim m^2/2\) . We prove that the row vector obtained by accumulating intermediate forms of the construction gives a minimal grlex Gröbner basis for \(\mathcal {I}_F\) for no extra computational cost other than storage (this is based on a closed-form description of a ’form vector’ for F, an associated vector of total degrees and a syzygy triple derived from the construction. These imply that the remainder of the S polynomial of \(f_1,f_2\) is zero. Then we inductively apply Buchberger’s Criterion to show that the form vector yields a minimal Gb for \(\mathcal {I}_F\) ). We apply this to determining \(\dim _\mathbbm {k}(\mathbbm {k}[x,z] /\mathcal {I}_F)\) . We show that either the form vector is reduced or a monomial of \(f_1\) can be reduced by \(f_2\) . This enables us to efficiently construct the unique reduced Gröbner basis for \(\mathcal {I}_F\) from the vector extension of our algorithm. Then we specialise to the inverse form of a finite sequence, obtaining generator forms for its annihilator ideal and a corresponding algorithm. We compute the intersection of two annihilator ideals using syzygies in \(\mathbbm {k}[x,z]^5\) . This improves a result of Althaler and Dür. Finally we show that dehomogenisation induces a one-to-one correspondence ( \(f_1\) ,
      PubDate: 2017-01-01
      DOI: 10.1007/s00200-016-0295-6
      Issue No: Vol. 28, No. 1 (2017)
       
  • Secret sharing schemes based on additive codes over GF (4)
    • Authors: Jon-Lark Kim; Nari Lee
      Pages: 79 - 97
      Abstract: Abstract A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed–Solomon code. SSSs based on linear codes have been studied by many researchers. However there is little research on SSSs based on additive codes. In this paper, we study SSSs based on additive codes over GF(4) and show that they require at least two steps of calculations to reveal the secret. We also define minimal access structures of SSSs from additive codes over GF(4) and describe SSSs using some interesting additive codes over GF(4) which contain generalized 2-designs.
      PubDate: 2017-01-01
      DOI: 10.1007/s00200-016-0296-5
      Issue No: Vol. 28, No. 1 (2017)
       
  • An improved method for determining the weight distribution of a family of
           q -ary cyclic codes
    • Authors: Gerardo Vega
      Abstract: Abstract The purpose of this work is to use an already known identity among the weight enumerator polynomials, in order to present an improved method for determining the weight distribution of a family of q-ary reducible cyclic codes, that generalize, in an easier way, the results in Yu and Liu (Des Codes Cryptogr 78:731–745, 2016).
      PubDate: 2017-04-18
      DOI: 10.1007/s00200-017-0318-y
       
  • Spaces of directed paths on pre-cubical sets
    • Authors: Krzysztof Ziemiański
      Abstract: Abstract The spaces of directed paths on the geometric realizations of pre-cubical sets, called also \(\square \) -sets, can be interpreted as the spaces of possible executions of Higher Dimensional Automata, which are models for concurrent computations. In this paper we construct, for a sufficiently good pre-cubical set K, a CW-complex \(W(K)_v^w\) that is homotopy equivalent to the space of directed paths between given vertices v, w of K. This construction is functorial with respect to K, and minimal among all functorial constructions. Furthermore, explicit formulas for incidence numbers of the cells of \(W(K)_v^w\) are provided.
      PubDate: 2017-03-02
      DOI: 10.1007/s00200-017-0316-0
       
  • Some cyclic codes from some monomials
    • Authors: Zohreh Rajabi; Kazem Khashyarmanesh
      Abstract: Abstract Cyclic codes are an important class of linear codes. The objectives of this paper are to earn and extend earlier results over cyclic codes from some monomials. In fact, we determine the dimension and the generator polynomial of the code \({\mathcal {C}}_s\) defined by the monomial \(f(x)=x^{\frac{p^h+1}{2}}\) over \({\mathrm {GF}}(p^m)\) , where p is an odd prime and h is an integer. Also, we provide some answers for Open Problems 5.26 and 5.30 in Ding (SIAM J Discrete Math 27:1977–1994, 2013). Moreover, we study the code \({\mathcal {C}}_s\) defined by the monomial \(f(x)=x^{\frac{q^h-1}{q-1}}\) over \(\mathrm {GF}(q^m)\) , where h is an integer, without any restriction on h (see Section 5.3 in the above mentioned paper).
      PubDate: 2017-03-01
      DOI: 10.1007/s00200-017-0317-z
       
  • 1-Generator quasi-cyclic and generalized quasi-cyclic codes over the ring
           $$\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1}\right\rangle }}$$
           Z 4 [ u ] u 2 - 1
    • Authors: Yun Gao; Jian Gao; Tingting Wu; Fang-Wei Fu
      Abstract: Abstract In this paper, we study 1-generator quasi-cyclic and generalized quasi-cyclic codes over the ring \(R=\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1} \right\rangle }}\) . We determine the structure of the generators and the minimal generating sets of 1-generator QC and GQC codes. We also give a lower bound for the minimum distance of free 1-generator quasi-cyclic and generalized quasi-cyclic codes over this ring, respectively. Furthermore, some new \(\mathbb {Z}_4\) -linear codes via the Gray map which have better parameters than the best known \(\mathbb {Z}_4\) -linear codes are presented.
      PubDate: 2017-02-20
      DOI: 10.1007/s00200-017-0315-1
       
  • A constructive test for exponential stability of linear time-varying
           discrete-time systems
    • Authors: Ulrich Oberst
      Abstract: Abstract We complete the stability results of the paper Bourlès et al. (SIAM J Control Optim 53:2725–2761, 2015), and for this purpose use the linear time-varying (LTV) discrete-time behaviors and the exponential stability (e.s.) of this paper. In the main theorem we characterize the e.s. of an autonomous LTV system by standard spectral properties of a complex matrix connected with the system. We extend the theory of discrete-time LTV behaviors, developed in the quoted publication, from the coefficient field of rational functions to that of locally convergent Laurent series or even of Puiseux series. The stability test can and has to be applied in connection with the construction of stabilizing compensators.
      PubDate: 2017-02-15
      DOI: 10.1007/s00200-017-0314-2
       
  • Several proofs of security for a tokenization algorithm
    • Authors: Riccardo Aragona; Riccardo Longo; Massimiliano Sala
      Abstract: Abstract In this paper we propose a tokenization algorithm of Reversible Hybrid type, as defined in PCI DSS guidelines for designing a tokenization solution, based on a block cipher with a secret key and (possibly public) additional input. We provide some formal proofs of security for it, which imply our algorithm satisfies the most significant security requirements described in PCI DSS tokenization guidelines. Finally, we give an instantiation with concrete cryptographic primitives and fixed length of the PAN, and we analyze its efficiency and security.
      PubDate: 2017-02-13
      DOI: 10.1007/s00200-017-0313-3
       
  • Performance of ternary double circulant, double twistulant, and self-dual
           codes
    • Authors: T. Aaron Gulliver; Masaaki Harada
      Abstract: Abstract We study the performance of ternary isodual codes which are not self-dual and ternary self-dual codes, as measured by the decoding error probability with bounded distance decoding. We compare the performance of ternary double circulant and double twistulant codes which are not self-dual with ternary extremal self-dual codes. We also investigate the performance of ternary self-dual codes having large minimum weights.
      PubDate: 2017-01-16
      DOI: 10.1007/s00200-017-0312-4
       
  • Computing Tjurina stratifications of $$\mu $$ μ -constant deformations
           via parametric local cohomology systems
    • Authors: Katsusuke Nabeshima; Shinichi Tajima
      Pages: 451 - 467
      Abstract: Abstract Algebraic local cohomology classes associated with parametric semi-quasihomogeneous hypersurface isolated singularities are considered in the context of symbolic computation. The motivations for this paper are computer calculations of complete lists of Tjurina numbers of semi-quasihomogeneous polynomials with isolated singularity. A new algorithm, that utilizes parametric local cohomology systems, is proposed to compute Tjurina stratifications associated with \(\mu \) -constant deformations of weighted homogeneous isolated singularities. The resulting algorithm gives in particular a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology systems. An efficient algorithm of computing parametric standard bases of relevant ideals is also given as an application of parametric local cohomology systems.
      PubDate: 2016-12-01
      DOI: 10.1007/s00200-016-0289-4
      Issue No: Vol. 27, No. 6 (2016)
       
  • Computing Tjurina stratifications of $$\mu $$ μ -constant deformations
           via parametric local cohomology systems
    • Authors: Katsusuke Nabeshima; Shinichi Tajima
      Pages: 451 - 467
      Abstract: Abstract Algebraic local cohomology classes associated with parametric semi-quasihomogeneous hypersurface isolated singularities are considered in the context of symbolic computation. The motivations for this paper are computer calculations of complete lists of Tjurina numbers of semi-quasihomogeneous polynomials with isolated singularity. A new algorithm, that utilizes parametric local cohomology systems, is proposed to compute Tjurina stratifications associated with \(\mu \) -constant deformations of weighted homogeneous isolated singularities. The resulting algorithm gives in particular a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology systems. An efficient algorithm of computing parametric standard bases of relevant ideals is also given as an application of parametric local cohomology systems.
      PubDate: 2016-12-01
      DOI: 10.1007/s00200-016-0289-4
      Issue No: Vol. 27, No. 6 (2016)
       
  • Undeniable signature scheme based over group ring
    • Authors: Neha Goel; Indivar Gupta; M. K. Dubey; B. K. Dass
      Pages: 523 - 535
      Abstract: Abstract D. Chaum and H. van Antwerpen first introduced the concept of an undeniable signature scheme where the verification step is verified with the signer’s co-operation. In this paper, first we discuss a combination of Discrete Logarithm Problem (DLP) and Conjugacy Search Problem (CSP) analysing its security. Then we propose an undeniable signature scheme in a non-abelian group over group ring whose security relies on difficulty of the combination of the DLP and the CSP. The complexity and security of our proposed scheme has also been discussed.
      PubDate: 2016-12-01
      DOI: 10.1007/s00200-016-0293-8
      Issue No: Vol. 27, No. 6 (2016)
       
  • Undeniable signature scheme based over group ring
    • Authors: Neha Goel; Indivar Gupta; M. K. Dubey; B. K. Dass
      Pages: 523 - 535
      Abstract: Abstract D. Chaum and H. van Antwerpen first introduced the concept of an undeniable signature scheme where the verification step is verified with the signer’s co-operation. In this paper, first we discuss a combination of Discrete Logarithm Problem (DLP) and Conjugacy Search Problem (CSP) analysing its security. Then we propose an undeniable signature scheme in a non-abelian group over group ring whose security relies on difficulty of the combination of the DLP and the CSP. The complexity and security of our proposed scheme has also been discussed.
      PubDate: 2016-12-01
      DOI: 10.1007/s00200-016-0293-8
      Issue No: Vol. 27, No. 6 (2016)
       
  • Hamming distances from a function to all codewords of a Generalized
           Reed-Muller code of order one
    • Authors: Miriam Abdón; Robert Rolland
      Abstract: Abstract For any finite field \({\mathbb {F}}_q\) with q elements, we study the set \({\mathscr {F}}_{(q,m)}\) of functions from \({\mathbb {F}}_q^m\) into \({\mathbb {F}}_q\) from geometric, analytic and algorithmic points of view. We determine a linear system of \(q^{m+1}\) equations and \(q^{m+1}\) unknowns, which has for unique solution the Hamming distances of a function in \({\mathscr {F}}_{(q,m)}\) to all the affine functions. Moreover, we introduce a Fourier-like transform which allows us to compute all these distances at a cost \(O(mq^m)\) and which would be useful for further problems.
      PubDate: 2016-12-24
      DOI: 10.1007/s00200-016-0311-x
       
  • Binary codes and permutation decoding sets from the graph products of
           cycles
    • Authors: W. Fish
      Abstract: Abstract Let \(n, m \ge 2\) be integers. The cartesian, categorical and lexicographic products of m copies of the n-cycle denoted by \(C_n\) all have as their vertex-set \(\{0, 1, \ldots , n-1\}^m\) , with adjacency defined variously. In this paper the binary codes generated by the row span of adjacency matrices of the cartesian, categorical and lexicographic products of m copies of \(C_n\) are examined. Full and partial PD-sets were also found for the various codes.
      PubDate: 2016-12-20
      DOI: 10.1007/s00200-016-0310-y
       
 
 
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