Cyclic codes over a non-chain ring Re,q and their application to LCD codes

被引：16

作者：

Islam, Habibul ^{[1
]}

Martinez-Moro, Edgar ^{[2
]}

Prakash, Om ^{[1
]}

机构：

[1] Indian Inst Technol Patna, Dept Math, Bihta, Bihar, India

[2] Univ Valladolid, Inst Math, Valladolid, Spain

来源：

DISCRETE MATHEMATICS | 2021年 / 344卷 / 10期

关键词：

Cyclic code; LCD code; Optimal code; MDS code; Self-dual code; Gray map; LINEAR CODES; DUAL CODES; Z(4);

D O I：

10.1016/j.disc.2021.112545

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-q be a finite field of order q, a prime power integer, such that q = et + 1 where t >= 1, e >= 2 are integers. In this paper, we study cyclic codes of length nover a non-chain ring R-e,R-q = F-q[u]/< u(e) - 1 >. We define a Gray map phi and obtain many maximum-distance-separable (MDS) and optimal F-q-linear codes from the Gray images of cyclic codes. Under certain conditions we determine linear complementary dual (LCD) codes of length n when gcd(n, q) not equal 1 and gcd(n, q) = 1, respectively. It is proved that a cyclic code C of length n is an LCD code if and only if its Gray image phi(C) is an LCD code of length en over F-q. Among others, we present the conditions for existence of free and non-free LCD codes. Moreover, we obtain many optimal LCD codes as the Gray images of non-free LCD codes over R-e,R-q. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：11

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