Quasi-cyclic codes as cyclic codes over a family of local rings

被引：4

作者：

Dougherty, Steven T. ^{[1
]}

Fernandez-Cordoba, Cristina ^{[2
]}

Ten-Valls, Roger ^{[2
]}

机构：

[1] Univ Scranton, Dept Math, Scranton, PA 18510 USA

[2] Univ Autonoma Barcelona, Dept Informat & Commun Engn, Bellaterra 08193, Spain

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2016年 / 40卷

关键词：

Quasi-cyclic codes; Codes over rings;

D O I：

10.1016/j.ffa.2016.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：138 / 149

页数：12

共 7 条

[1]

Dougherty S.T., 2013, EUR J PURE APPL MATH, V6

[2] Cyclic codes over Rk [J].