A Family of Constacyclic Codes over ■2m+u■2mand Its Application to Quantum Codes

被引：0

作者：

TANG Yongsheng ^{[1
]}

YAO Ting ^{[2
]}

ZHU Shixin ^{[2
]}

KAI Xiaoshan ^{[2
]}

机构：

[1] School of Mathematics and Statistics, Hefei Normal University

[2] School of Mathematics, Hefei University of Technology

来源：

Chinese Journal of Electronics | 2020年 / 29卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Constacyclic codes; Cyclic codes; Quasicyclic codes; Gray map; Quantum codes;

D O I：

暂无

中图分类号：

TN911.22 [信道编码理论];

学科分类号：

070104 ; 081101 ;

摘要：

Let R be the ring ■2m+u■2m,where u2=0.We introduce a Gray map from R to ■22m and study(1+u)-constacyclic codes over R.It is proved that the image of a(1+u)-constacyclic code length n over R under the Gray map is a distance-invariant binary quasicyclic code of index m and length 2 mn.We also prove that every code of length 2 mn which is the Gray image of cyclic codes over R of length n is permutation equivalent to a binary quasi-cyclic code of index m.Furthermore,a family of quantum error-correcting codes obtained from the Calderbank-Shor-Steane(CSS) construction applied to(1+u)-constacyclic codes over R.

引用

页码：114 / 121

页数：8

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