On cyclic codes over Galois rings

被引：6

作者：

Kaur, Jasbir ^{[1
]}

Dutt, Sucheta ^{[1
]}

Sehmi, Ranjeet ^{[1
]}

机构：

[1] PEC Univ Technol, Dept Appl Sci, Chandigarh, India

来源：

DISCRETE APPLIED MATHEMATICS | 2020年 / 280卷

关键词：

Galois ring; Cyclic codes; Grobner basis; Minimal degree polynomial; Torsion codes; STRONG GROBNER BASES; NEGACYCLIC CODES;

D O I：

10.1016/j.dam.2018.01.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a Galois ring of characteristic p(a), where p is a prime and a is a natural number. In this paper, the generators of cyclic codes of arbitrary length n over R in terms of minimal degree polynomials of certain subsets of codes have been obtained. Moreover, the explicit set of generators so obtained turns out to be a minimal strong Grobner basis. Some results on torsion codes of a cyclic code over R have also been obtained. Using these results, the size of a cyclic code over R has been expressed in terms of the degrees of its generators. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：156 / 161

页数：6

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