Additive cyclic codes over finite commutative chain rings

被引：6

作者：

Martinez-Moro, Edgar ^{[1
]}

Otal, Kamil ^{[2
,3
]}

Ozbudak, Ferruh ^{[2
,3
]}

机构：

[1] Univ Valladolid, Math Res Inst, Castilla, Spain

[2] Middle East Tech Univ, Dept Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey

[3] Middle East Tech Univ, Inst Appl Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey

来源：

DISCRETE MATHEMATICS | 2018年 / 341卷 / 07期

关键词：

Cyclic codes; Additive codes; Codes over rings; Finite commutative chain rings; Galois rings; MULTIVARIABLE CODES; GALOIS RINGS; CONSTRUCTION; PREPARATA; KERDOCK;

D O I：

10.1016/j.disc.2018.03.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1873 / 1884

页数：12

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