Quantum codes from cyclic codes over the ring Fq+v1Fq++vrFq

被引：0

作者：

Gao, Yun ^{[1
,2
]}

Gao, Jian ^{[3
]}

Fu, Fang-Wei ^{[1
,2
]}

机构：

[1] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[3] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Peoples R China

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2019年 / 30卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Quantum codes; Cyclic codes; Dual containing codes; Gray map; NONBINARY; CONSTRUCTION;

D O I：

10.1007/s00200-018-0366-y

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Let R=Fq+v1Fq++vrFq, where q is a power of a prime, vi2 0 for 1i,jr and r1. In this paper, the structure of cyclic codes over the ring R is studied and a Gray map phi from Rn to Fq(r+1)n is given. We give a construction of quantum codes from cyclic codes over the ring R. We derive Euclidean dual containing codes over Fq and Hermitian dual containing codes over Fp2m as Gray images of cyclic codes over R. In particular, we use r+1 codes associated with a cyclic code over R of arbitrary length to determine the parameters of the corresponding quantum code. Furthermore, some new non-binary quantum codes are obtained.

引用

页码：161 / 174

页数：14

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