Results 1 to 10 of about 513,670 (123)
Polyadic Constacyclic Codes [PDF]
IEEE Transactions on Information Theory, 2015 We provide complete solutions on two basic questions on polyadic constacyclic cdes, and construct some optimal codes from the polyadic constacyclic ...
San Ling, Yun Fan, Hai Dinh
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Application of Constacyclic Codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2015 Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction and the quantum Singleton bound. If $C^{\perp_{H}}\subseteq C$, we say that $C$ is a dual-containing
Bocong Chen, San Ling, Guanghui Zhang
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MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes [PDF]
IEEE Access, 2021 Symbol-pair codes are used to protect against symbol-pair errors in high density data storage systems. One of the most important tasks in symbol-pair coding theory is to design MDS codes. MDS symbol-pair codes are optimal in the sense that such codes attain the Singleton bound. In this paper, a new class of MDS symbol-pair codes with code-length $5p$
Hai Q. Dinh 0001 +3 more
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Quantum Codes Obtained from Skew ϱ‐λ‐Constacyclic Codes over Rk
Quantum Engineering, Volume 2023, Issue 1, 2023., 2023 Let Rk=Fqu1,u2,⋯,uk/
Bo Kong +4 more
wiley +1 more source
Characterizations and Properties of Monic Principal Skew Codes over Rings
Security and Communication Networks, Volume 2022, Issue 1, 2022., 2022 Let A be a ring with identity, σ a ring endomorphism of A that maps the identity to itself, δ a σ‐derivation of A, and consider the skew‐polynomial ring A[X; σ, δ]. When A is a finite field, a Galois ring, or a general ring, some fairly recent literature used A[X; σ, δ] to construct new interesting codes (e.g., skew‐cyclic and skew‐constacyclic codes ...
Mhammed Boulagouaz +2 more
wiley +1 more source
Matrix‐Product Codes over Commutative Rings and Constructions Arising from (σ, δ)‐Codes
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 A well‐known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix‐product code (MPC) is shown to remain valid over any commutative ring R. A sufficient condition is given, as well, for such a bound to be sharp. It is also shown that an MPC is free when its input codes are all free, in which case
Mhammed Boulagouaz +2 more
wiley +1 more source
A generalization of cyclic code equivalence algorithm to constacyclic codes
Designs, Codes and Cryptography, 2022 Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we found many constacyclic codes with good parameters and properties. In particular, we found 23 new codes that improve
Dev Akre +3 more
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Galois self-dual constacyclic codes [PDF]
Designs, Codes and Cryptography, 2016 Key words: Constacyclic code, Galois inner product, $q$-coset function, isometry, Galois self-dual ...
Yun Fan, Liang Zhang
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Skew Constacyclic Codes over Finite Fields and Finite Chain Rings
Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 This paper overviews the study of skew Θ‐λ‐constacyclic codes over finite fields and finite commutative chain rings. The structure of skew Θ‐λ‐constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skew Θ‐cyclic and skew Θ‐negacyclic codes over finite chain rings in general and ...
Hai Q. Dinh +3 more
wiley +1 more source
Hermitian Self‐Orthogonal Constacyclic Codes over Finite Fields
Journal of Discrete Mathematics, Volume 2014, Issue 1, 2014., 2014 Necessary and sufficient conditions for the existence of Hermitian self‐orthogonal constacyclic codes of length n over a finite field Fq2, n coprime to q, are found. The defining sets and corresponding generator polynomials of these codes are also characterised. A formula for the number of Hermitian self‐orthogonal constacyclic codes of length n over a
Amita Sahni +2 more
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