منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
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In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
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We study the structure of linear codes over the ring Bk which is defined by Fpr [v1, v2, . . . , vk]/〈v 2 i = vi, viv j = v jvi〉 k i, j=1. In order to study the codes, we begin with studying the structure of the ring Bk via a Gray map which also induces a relation between codes over Bk and codes over Fpr . We consider Euclidean and Hermitian self-dual codes, MacWilliams relations, as well as Si...
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Abstract: Let Rk,m be the ring F2m [u1, u2, · · · , uk]/ ⟨ ui , uiuj − ujui ⟩ . In this paper, cyclic codes of arbitrary length n over the ring R2,m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m -basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one...
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ژورنال
عنوان ژورنال: IEEE Access
سال: 2020
ISSN: 2169-3536
DOI: 10.1109/access.2020.2989203