Ideal Structure of Zq + uZq and Zq + uZq-Cyclic Codes

被引：2

作者：

Kumar, Raj ^{[1
]}

Bhaintwal, Maheshanand ^{[1
]}

Bandi, Ramakrishna ^{[2
]}

机构：

[1] Indian Inst Technol Roorkee, Dept Math, Roorkee, Uttar Pradesh, India

[2] Int Inst Informat Pchnol, Dept Math, Naya Raipur, India

来源：

FILOMAT | 2020年 / 34卷 / 12期

关键词：

cyclic codes; codes over rings; self-dual codes; CYCLIC CODES;

D O I：

10.2298/FIL2012199K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study cyclic codes of length n over R = Z(q) + uZ(q), u(2) = 0, where q is a power of a prime p and (n, p) = 1. We have determined the complete ideal structure of R. Using this, we have obtained the structure of cyclic codes and that of their duals through the factorization of x(n) - 1 over R. We have also computed total number of cyclic codes of length n over R. A necessary and sufficient condition for a cyclic code over R to be self-dual is presented. We have presented a formula for the total number of self-dual cyclic codes of length n over R. A new Gray map from R to Z(p)(2r) is defined. Using Magma, some good cyclic codes of length 4 over Z(9) + uZ(9) are obtained.

引用

页码：4199 / 4214

页数：16

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