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Constacyclic codes over 𝔽q𝒮𝒯 and their applications
AKCE International Journal of Graphs and CombinatoricsLet [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text].
Amal S. Alali +3 more
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DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
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Double Constacyclic Codes over Two Finite Commutative Chain Rings [PDF]
, 2022 Yun Fan, Hualu Liu
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Skew Constacyclic Codes over Galois Rings
Advances in Mathematics of Communications, 2008 We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied.
Delphine Boucher +2 more
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Two Classes of Constacyclic Codes With a Square-Root-Like Lower Bound [PDF]
IEEE Transactions on Information TheoryConstacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this
Ting Chen +4 more
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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 +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 +5 more
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Galois Self-Dual 2-Quasi Constacyclic Codes Over Finite Fields [PDF]
IEEE Transactions on Information TheoryLet F be a field with cardinality $p^{\ell } $ and $0\neq \lambda \in F$ , and $0\le h\lt \ell $ . Extending Euclidean and Hermitian inner products, Fan and Zhang introduced Galois $p^{h}$ -inner product (DCC, vol.84, pp.473–492).
Yun Fan, Yue Leng
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet 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 +3 more
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