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 ...
متن کاملStructure of linear codes over the ring Bk
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...
متن کاملOn Skew Cyclic Codes over a Finite Ring
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.
متن کاملLinear Algebra over a Ring
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with coefficients in R. In the case when the ring R is a field, every pair is equivalent to a homogeneous system. Using the formal matrix calculus, two alternate pr...
متن کاملNew Ring-Linear Codes from Geometric Dualization
In the 1960s and 1970s the Nordstrom-Robinson-Code [30] and subsequently the infinite series of the Preparata[31], Kerdock[21], Delsarte-Goethals[6] and Goethals-Codes [7] were discovered. Apart from a few corner cases, all of these codes are non-linear binary block codes that have higher minimum distance than any known comparable (having equal size and length) linear binary code. We will call ...
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ژورنال
عنوان ژورنال: DEStech Transactions on Computer Science and Engineering
سال: 2018
ISSN: 2475-8841
DOI: 10.12783/dtcse/iece2018/26646