On normalized generating sets for GQC codes over Z2

被引：5

作者：

Bae, Sunghan ^{[1
]}

Kang, Pyung-Lyun ^{[2
]}

Li, Chengju ^{[3
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math, Daejeon 34141, South Korea

[2] Chungnam Natl Univ, Dept Math, Daejeon 34134, South Korea

[3] East China Normal Univ, Sch Comp Sci & Software Engn, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2017年 / 45卷

关键词：

Binary codes; Generalized quasi-cyclic codes; Dual codes; QUASI-CYCLIC CODES; STRUCTURAL-PROPERTIES;

D O I：

10.1016/j.ffa.2016.11.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let r(i), be positive integers and R-i = Z(2)[x]/ < x(ri) - 1 > for 1 <= i <= l. Denote R = R-1 x R-2 x ... x R-l. Generalized quasi-cyclic (GQC) code C of length (r(1), r(2),..., r(l)) over Z(2) can be viewed as Z(2) [x]-submodule of R. In this paper, we investigate the algebraic structure of C by presenting its normalized generating set. We also present a method to determine the normalized generating set of the dual code of C, which is derived from the normalized generating set of C. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：285 / 300

页数：16

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