Subjects -> MATHEMATICS (Total: 1013 journals)
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MATHEMATICS (714 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)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
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: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 4)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 21)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 7)
Advances in Materials Science     Open Access   (Followers: 23)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 7)
Algorithms     Open Access   (Followers: 15)
Algorithms Research     Open Access   (Followers: 2)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
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: 3)
Annals of Data Science     Hybrid Journal   (Followers: 17)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
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   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
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: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 17)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 22)
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  
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: 5)
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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
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  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 3)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
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: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
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  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
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  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 22)
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: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 12)
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: 12)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
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  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Cryptography and Communications
Journal Prestige (SJR): 0.446
Citation Impact (citeScore): 1
Number of Followers: 11  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1936-2455 - ISSN (Online) 1936-2447
Published by Springer-Verlag Homepage  [2467 journals]
  • Correction to: Galois hulls of constacyclic codes over finite fields

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      Abstract: A Correction to this paper has been published: https://doi.org/10.1007/s12095-022-00602-6
      PubDate: 2023-02-01
       
  • Reconstruction of permutations distorted by single Kendall τ-errors

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      Abstract: Abstract Levenshtein first put forward the sequence reconstruction problem in 2001. This problem sets a model in which a sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. In this model, the sequence reconstruction problem is to find the minimum number of channels required to exactly recover the transmitted sequence. In the combinatorial context, the problem is equivalent to determining the maximum intersection between two balls of radius r, where the distance between their centers is at least d. The sequence reconstruction problem was studied for strings, permutations and so on. In this paper, we extend the study by Konstantinova et al. for reconstruction of permutations distorted by single Kendall τ-errors. While they solved the case where the transmitted permutation can be arbitrary and the erroneous patterns are distorted by at most two Kendall τ-errors, we study the setup where the transmitted permutation belongs to a permutation code of length n and the erroneous patterns are distorted by at most three Kendall τ-errors. In this scenario, it is shown that n2 − n + 1 erroneous patterns are required in order to reconstruct an unknown permutation from some permutation code of minimum Kendall τ-distance 2 or an arbitrary unknown permutation for any n ≥ 3.
      PubDate: 2023-02-01
       
  • Multi-twisted additive codes over finite fields are asymptotically good

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      Abstract: Abstract Multi-twisted (MT) additive codes over finite fields constitute a special class of additive codes and are generalizations of cyclic additive codes. In this paper, we study a class of 1-generator MT additive codes over finite fields. We further study the asymptotic behaviour of the rates and relative Hamming distances of a certain special subclass of 1-generator MT additive codes by using probabilistic methods. We show that there exists an asymptotically good infinite sequence of MT additive codes of length pγℓ with block length \(p^{\gamma } \to \infty\) over \(\mathbb {F}_{q^{t}}\) of rate \(0<\frac {f}{\ell t p^{d}}<1\) and relative Hamming distance at least δ, where ℓ ≥ 1 and t ≥ 2 are integers, q is a prime power, \(\mathbb {F}_{q^{t}}\) is the finite field of order qt, p is an odd prime satisfying \(\gcd (p,q)=\gcd (p,q-1)=1,\) f is the multiplicative order of q modulo p, d is the largest positive integer such that pd divides qf − 1, γ is a positive integer satisfying γ ≥ d + 1, and δ is a positive real number satisfying \(h_{q^{t}}(\delta ) < 1-\frac {1}{\ell t},\) (here \(h_{q^{t}}\) denotes the qt-ary entropy function). This shows that the family of MT additive codes over finite fields is asymptotically good.
      PubDate: 2023-02-01
       
  • Constructions of almost complementary pairs based on non-standard Golay
           sequences

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      Abstract: Abstract Almost complementary pairs (ACPs) are sequence pairs having zero aperiodic autocorrelation sums at all non-zero time-shifts except only one position. These are generalizations of the well-known Golay complementary pairs (GCPs). To date, known ACPs have been constructed via standard Golay sequences (GSs). In this paper, we construct novel quaternary and 16-QAM ACPs of non-power-of-two lengths based on non-standard GSs. It turns out that the peak-to-mean envelope power ratios (PMEPRs) of the proposed ACPs are upper bounded by 3.34. Due to their good correlation and low PMEPR properties, ACPs could be used as an alternative to GCPs in practical applications.
      PubDate: 2023-02-01
       
  • Generalized block inserting for constructing new constant dimension codes

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      Abstract: Abstract Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. A fundamental problem for CDCs is to explore the maximum possible cardinality Aq(n,d,k) of a set of k-dimensional subspaces in \(\mathbb {F}^{n}_{q}\) such that the subspace distance statisfies dis(U,V ) = 2k − 2 dim(U ∩ V ) ≥ d for all pairs of distinct subspaces U and V in this set. In this paper, by means of an appropriate combination of the matrix blocks from rank metric codes and small CDCs, we present three constructions of CDCs based on the generalized block inserting construction by Niu et al. in 2021. According to our constructions, we obtain 28 new lower bounds for CDCs which are better than the previously known lower bounds.
      PubDate: 2023-02-01
       
  • Hermitian dual-containing constacyclic codes over $$\mathbb
           {F}_{q^{2}}+{v_{1}}\mathbb {F}_{q^{2}}+\cdots +{v_{r}}\mathbb
           {F}_{q^{2}}$$ and new quantum codes

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      Abstract: Abstract In this paper, we study Hermitian dual-containing constacyclic codes over the finite ring \(R_{r}=\mathbb {F}_{q^{2}}+{v_{1}}\mathbb {F}_{q^{2}}+\cdots +{v_{r}}\mathbb {F}_{q^{2}}\) , where q is a prime power and \({v_{i}}^{2}={v_{i}},v_{i}v_{j}=v_{j}v_{i}=0\) for 1 ≤ i,j ≤ r,i≠j. A necessary and sufficient condition is provided to determine whether a constacyclic code C over Rr is Hermitian dual-containing. Moreover, we propose a generalized Gray map ΦM to preserve the property of Hermitian dual-containing. Compared with some existing Gray maps, ΦM increases the possibility of making the minimum distance of ΦM(C) larger. As an application, some new quantum codes over \(\mathbb {F}_{q}\) are constructed from constacyclic codes over Rr.
      PubDate: 2023-02-01
       
  • A direct construction of even length ZCPs with large ZCZ ratio

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      Abstract: Abstract This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). The applicability of ZCPs increases with the increasing value of ZCZ width, which plays a significant role in reducing interference in a communication system with asynchronous surroundings. For q = 2, the proposed ZCPs reduce to even length binary ZCPs (EB-ZCPs). However, to the best of the authors’ knowledge, the highest ZCZ ratio for even length ZCPs which are directly constructed to date using GBFs is 3/4. In the proposed construction, we provide even length ZCPs with ZCZ ratios 5/6 and 6/7, which are the largest ZCZ ratios achieved to date through direct construction.
      PubDate: 2023-02-01
       
  • New frequency-hopping sequence sets with good parameters under aperiodic
           hamming correlation

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      Abstract: Abstract In this paper, two constructions of frequency-hopping sequence (FHS for short) sets with respect to aperiodic Hamming correlation (AHC for short) are presented. Based on the presented constructions, we obtain several classes of optimal or near optimal FHS sets from cyclic codes and some known FHS sets with periodic partial Hamming correlation (PPHC for short), and explicitly determine their parameters. Moreover, the parameters of the obtained FHS sets are new and have large family size.
      PubDate: 2023-02-01
       
  • On decompositions of permutation polynomials into quadratic and cubic
           power permutations

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      Abstract: Abstract Decomposing permutation polynomials into power permutations of small algebraic facilitates the reduction of hardware area requirements when symmetric cryptographic algorithms are implemented with countermeasures to side channel attacks in mind. Our contribution in this work is twofold. Firstly, we determine such decompositions into power permutations of the field \({\mathbb F}_{2^{n}}\) of degree at most 2 for infinitely many odd n satisfying a specific property. Secondly, after improving the complexity of an existing algorithm, we use it to complete the list of known shortest decompositions of the inversion in \({\mathbb F}_{2^{n}}\) up to n = 32, and show that always considering degrees at most 3 can lead to shorter lengths or smaller area requirements.
      PubDate: 2023-02-01
       
  • Galois hulls of constacyclic codes over finite fields

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      Abstract: Abstract This paper presents a formula for the dimension of Galois hulls of constacyclic codes. For this, we have arranged the irreducible factors of xn − λ over the finite field \(\mathbb {F}_{q}\) in a suitable way. Also, considering some restrictions on q, the number of constacyclic codes of length n over \(\mathbb {F}_{q}\) is calculated for a given Galois hull dimension.
      PubDate: 2023-02-01
       
  • Triplicate functions

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      Abstract: Abstract We define the class of triplicate functions as a generalization of 3-to-1 functions over \(\mathbb {F}_{2^{n}}\) for even values of n. We investigate the properties and behavior of triplicate functions, and of 3-to-1 among triplicate functions, with particular attention to the conditions under which such functions can be APN. We compute the exact number of distinct differential sets of power APN functions and quadratic 3-to-1 functions; we show that, in this sense, quadratic 3-to-1 functions are a generalization of quadratic power APN functions for even dimensions, in the same way that quadratic APN permutations are generalizations of quadratic power APN functions for odd dimensions. We show that quadratic 3-to-1 APN functions cannot be CCZ-equivalent to permutations in the case of doubly-even dimensions. We compute a lower bound on the Hamming distance between any two quadratic 3-to-1 APN functions, and give an upper bound on the number of such functions over \(\mathbb {F}_{2^{n}}\) for any even n. We survey all known infinite families of APN functions with respect to the presence of 3-to-1 functions among them, and conclude that for even n almost all of the known infinite families contain functions that are quadratic 3-to-1 or are EA-equivalent to quadratic 3-to-1 functions. We also give a simpler univariate representation in the case of singly-even dimensions of the family recently introduced by Göloglu than the ones currently available in the literature. We conduct a computational search for quadratic 3-to-1 functions in even dimensions n ≤ 12. We find six new APN instances for n = 10, and the first sporadic APN instance for n = 12 since 2006. We provide a list of all known 3-to-1 APN functions for n ≤ 12.
      PubDate: 2023-02-01
       
  • On a class of skew constacyclic codes over mixed alphabets and
           applications in constructing optimal and quantum codes

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      Abstract: Abstract In this paper, we first discuss linear codes over R and present the decomposition structure of linear codes over the mixed alphabet \(\mathbb {F}_{q}R\) , where \(R=\mathbb {F}_{q}+u\mathbb {F}_{q}+v\mathbb {F}_{q}+uv\mathbb {F}_{q}\) , with u2 = 1,v2 = 1, uv = vu and q = pm for odd prime p, positive integer m. Let 𝜃 be an automorphism on \(\mathbb {F}_{q}\) . Extending 𝜃 to Θ over R, we study skew (𝜃,Θ)-(λ,Γ)-constacyclic codes over \(\mathbb {F}_{q}R\) , where λ and Γ are units in \(\mathbb {F}_{q}\) and R, respectively. We also show that, the dual of a skew (𝜃,Θ)-(λ,Γ)-constacyclic code over \(\mathbb {F}_{q}R\) is a skew (𝜃,Θ)-(λ− 1,Γ− 1)-constacyclic code over \(\mathbb {F}_{q}R\) . We classify some self-dual skew (𝜃,Θ)-(λ,Γ)-constacyclic codes using the possible values of units of R. Also using suitable values of λ,𝜃,Γ and Θ, we present the structure of other linear codes over \(\mathbb {F}_{q} R\) . We construct a Gray map over \(\mathbb {F}_{q}R\) and study the Gray images of skew (𝜃,Θ)-(λ,Γ)-constacyclic codes over \(\mathbb {F}_{q}R\) . As applications of our study, we construct many good codes, among them, there are 17 optimal codes and 2 near-optimal codes. Finally, we discuss the advantages in a construction of quantum error-correcting codes (QECCs) from skew 𝜃-cyclic codes than from cyclic codes over \(\mathbb {F}_{q}\) .
      PubDate: 2023-02-01
       
  • Symbol-pair weight distribution of some irreducible cyclic codes

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      Abstract: Abstract In this paper, we study the symbol-pair weight distribution of some irreducible cyclic codes. We define generalized cyclotomic numbers and provide some of their properties. Using a character sum, we establish a relationship among the symbol-pair weight of irreducible cyclic codes, generalized cyclotomic numbers and the Gaussian periods. Moreover, we determine the symbol-pair weight distribution of some classes of irreducible cyclic codes.
      PubDate: 2023-02-01
       
  • MDS constacyclic codes of length q + 1 over GF(q)

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      Abstract: Abstract MDS constacyclic codes over finite fields are important in both theory and practice. In this paper, all [q + 1,2,q] and [q + 1,3,q − 1] MDS λ-constacyclic codes over GF(q) are characterized, three classes of [q + 1,4,q − 2] MDS λ-constacyclic codes over GF(q) are constructed, and four classes of [q + 1,k,q − k + 2] MDS λ-constacyclic codes over GF(q) for variable k are presented. Rationales for distinguishing the class of cyclic codes, the class of λ-constacyclic codes with λ≠ 1, and the class of non-constacyclic linear codes are given. Some applications of MDS codes in cryptography are also summarised.
      PubDate: 2023-01-13
       
  • Octanary linear codes using simplicial complexes

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      Abstract: Abstract Certain simplicial complexes are used to construct a subset D of \(\mathbb {F}_{2^{n}}^{m}\) and D, in turn, defines the linear code CD over \(\mathbb {F}_{2^{n}}\) that consists of (v ⋅ d)d∈D for \(v\in \mathbb {F}_{2^{n}}^{m}\) . Here we deal with the case n = 3, that is, when CD is an octanary code. We establish a relation between CD and its binary subfield code \(C_{D}^{(2)}\) with the help of a generator matrix. For a given length and dimension, a code is called distance optimal if it has the highest possible distance. With respect to the Griesmer bound, three infinite families of distance optimal codes are obtained, and sufficient conditions for certain linear codes to be minimal are established.
      PubDate: 2022-12-22
       
  • On MDS codes with galois hulls of arbitrary dimensions

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      Abstract: Abstract The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois hulls of arbitrary dimensions via (extended) GRS codes. Four general methods of constructing MDS codes with Galois hulls of arbitrary dimensions by Hermitian or general Galois self-orthogonal (extended) GRS codes are given. Using these methods, some MDS codes with larger dimensions and Galois hulls of arbitrary dimensions can be obtained. In addition, two new classes of MDS codes with explicit parameters and with Galois hulls of arbitrary dimensions are also constructed. One of the two classes can yield 1-Galois self-orthogonal GRS codes, and more new classes of MDS codes with Galois hulls of arbitrary dimensions can be derived from one of the four general methods we give.
      PubDate: 2022-12-17
       
  • On the classification of ideals over $R[X]/\langle f(X)^{p^{s}}\rangle $
           when $R=\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+\ldots +u^{n}\mathbb
           {F}_{p^{m}}$

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      Abstract: Abstract In this paper, we give a general form of ideals over \(R[X]/\langle f(X)^{p^{s}}\rangle \) when f is a monic irreducible polynomial in R[X] and \(R= \mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+\ldots +u^{n}\mathbb {F}_{p^{m}}\) with un+ 1 = 0. For f(X) = X − 1 this gives a general form of cyclic codes over R. Furthermore, we apply the result to classify completely the cyclic codes of length 5ps over \(\mathbb {F}_{p^{m}}+u\mathbb {F}_{p^{m}}+u^{2}\mathbb {F}_{p^{m}}\) when p ≡ 2 (mod 5) or p ≡ 3 (mod 5) and m is odd.
      PubDate: 2022-12-17
       
  • A construction of optimal locally recoverable codes

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      Abstract: Abstract Locally recoverable codes are widely used in distributed and cloud storage systems. In this paper, we first present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out that the near MDS codes and their duals are both distance-optimal and dimension-optimal locally recoverable codes. The lengths of the locally recoverable codes are different from known ones in the literature.
      PubDate: 2022-12-05
       
  • Self-dual and LCD double circulant and double negacirculant codes over a
           family of finite rings $ \mathbb {F}_{q}[v_{1}, v_{2},\dots ,v_{t}]$

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      Abstract: Abstract In this paper, we discuss double circulant and double negacirculant codes over a family of finite rings \(R_{t} = \mathbb {F}_{q} + v_{1} \mathbb {F}_{q} + v_{2}\mathbb {F}_{q} + {\cdots } + v_{t}\mathbb {F}_{q}\) ; \(({v_{i}^{2}} = v_{i}, v_{i}v_{j} = v_{j}v_{i}=0, i,j= 1,2,\ldots ,t, i \neq j)\) , where q is an odd prime power. We obtain necessary and sufficient conditions for double circulant codes (double negacirculant codes) to be self-dual codes and to be linear codes with complementary dual (or LCD codes) codes and study the algebraic structure of self-dual and LCD double circulant (double negacirculant codes) codes. We derive a formula to determine the total number of self-dual and LCD double circulant codes (double negacirculant codes) over the ring Rt. We also find distance bounds for double circulant codes over Rt. Moreover, we use a Gray map to prove that the families of self-dual and LCD double circulant codes under this Gray map are asymptotically good.
      PubDate: 2022-12-03
       
  • New upper bounds and constructions of multi-erasure locally recoverable
           codes

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      Abstract: Abstract Multi-erasure locally recoverable codes (ME-LRCs) are an important class of locally recoverable codes (LRCs) with more constraints on the parameters. In this work, we present a new upper bound for ME-LRCs, which is tighter than that proposed by Cadambe and Mazumdar. The technique is to utilize the largest possible weight of linear codes to control the minimum distance. In addition, we present explicit constructions of ME-LRCs to achieve the proposed bound.
      PubDate: 2022-12-02
       
 
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