Results 51 to 60 of about 1,030 (123)

On optimal constacyclic codes

Linear Algebra and its Applications, 2016
In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal parameters.
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Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes

IEEE Access, 2019
Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that ...
Jianzhang Chen, Youqin Chen, Chunhui Feng, Yuanyuan Huang, Riqing Chen   +4 more
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Constacyclic codes over 𝔽pm[u1, u2,⋯,uk]/〈 ui2 = ui, uiuj = ujui〉

Open Mathematics, 2018
In this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈ui2$\begin{array}{} u^{2}_{i} \end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k.
Zheng Xiying, Kong Bo
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Applications of Constacyclic Codes to Some New Entanglement-Assisted Quantum MDS Codes

IEEE Access, 2019
Generally, it is not easy to construct quantum maximal-distance-separable (MDS) codes with the minimum distance greater than $\frac {q}{2}+1$ . The minimum distance of quantum MDS codes can achieve $\frac {q}{2}+1$ or exceed $\frac {q}{2}+1$ by ...
Jianzhang Chen, Youqin Chen, Dong Yu, Chunhui Feng, Yuanyuan Huang, Riqing Chen   +5 more
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$\lambda$-CONSTACYCLIC CODES OVER FINITE KRASNER HYPERFIELDS

Facta Universitatis, Series: Mathematics and Informatics, 2022
The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes.  In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial.
Tahan, Madeleine Al, Davvaz, Bijan
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The study of ℤpℤp[u, v]-additive cyclic codes and their application in obtaining Optimal and MDSS codes

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Let S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes.
Ashraf Mohammad, Asim Mohd, Mohammad Ghulam, Rehman Washiqur   +3 more
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γ-Dual Codes over Finite Commutative Chain Rings

Axioms
In this article, the notion of γ-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of γ-dual codes over finite chain rings are explored.
Hai Q. Dinh, Hiep L. Thi, Roengchai Tansuchat   +2 more
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Quantum Codes as an Application of Constacyclic Codes

Axioms
The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p.
Mohd Arif Raza, Mohammad Fareed Ahmad, Adel Alahmadi, Widyan Basaffar, Manish K. Gupta, Nadeem ur Rehman, Abdul Nadim Khan, Hatoon Shoaib, Patrick Sole   +8 more
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Construction of New Matrix-Product Codes and Their Applications

IEEE Access, 2019
In this paper, from special code chains $\mathcal {C}_{1} \supseteq \mathcal {C}_{2}~\supseteq \mathcal {C}_{3}$ such that $\mathcal {C}^{\bot _{h}}_{1}\subseteq \mathcal {C}_{3}$ and $\mathcal {C}^{\bot _{h}}_{2}\subseteq \mathcal {C}_{2}$ , some ...
Hao Song, Ruihu Li, Junli Wang, Jingjie Lv   +3 more
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