On the structure of cyclic codes over the ring Z2s[u]/⟨uk⟩

被引：5

作者：

Dinh, Hai Q. ^{[1
,2
,3
]}

Singh, Abhay Kumar ^{[4
]}

Kumar, Pratyush ^{[4
]}

Sriboonchitta, Songsak ^{[5
]}

机构：

[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[3] Kent State Univ, Dept Math Sci, 4314 Mahoning Ave, Warren, OH 44483 USA

[4] Indian Inst Technol ISM, Dept Appl Math, Dhanbad 826004, Bihar, India

[5] Chiang Mai Univ, Fac Econ, Chiang Mai 52000, Thailand

来源：

DISCRETE MATHEMATICS | 2018年 / 341卷 / 08期

关键词：

Cyclic codes; Dual codes; Self-dual codes; Codes over rings; Chain rings; Local rings; SELF-DUAL CODES; Z(4); PREPARATA; KERDOCK;

D O I：

10.1016/j.disc.2018.04.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R = Z(2s)[u]/< u(k)> = Z(2s) + uZ(2s) + ... + U(k-1)Z(2s) (u(k) = 0), for any integers s >= 1 and k >= 2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the duals of all cyclic codes. Among others, all self-dual cyclic codes of odd length n over the ring R are determined. Moreover, some examples are provided which produce several optimal codes. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2243 / 2275

页数：33

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