New q-ary quantum MDS codes with distances bigger than q/2

被引：1

作者：

He, Xianmang ^{[1
]}

Xu, Liqing ^{[2
]}

Chen, Hao ^{[2
]}

机构：

[1] Ningbo Univ, Sch Informat Sci & Technol, Ningbo 315211, Zhejiang, Peoples R China

[2] Hangzhou Dianzi Univ, Sch Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

QUANTUM INFORMATION PROCESSING | 2016年 / 15卷 / 07期

关键词：

Quantum MDS code; Hermitian self-orthogonal code; Generalized Reed-Solomon code; CONSTACYCLIC CODES;

D O I：

10.1007/s11128-016-1311-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The construction of quantum MDS codes has been studied by many authors. We refer to the table in page 1482 of (IEEE Trans Inf Theory 61(3):1474-1484, 2015) for known constructions. However, there have been constructed only a few q-ary quantum MDS [[n, n - 2d + 2, d]](q) codes with minimum distances d > q/2 for sparse lengths n > q + 1. In the case n = q(2)-1/m where m vertical bar q + 1 or m vertical bar q - 1 there are complete results. In the case n = q(2)-1/m while m vertical bar q(2) - 1 is neither a factor of q - 1 nor q + 1, no q-ary quantum MDS code with d > q/2 has been constructed. In this paper we propose a direct approach to construct Hermitian self-orthogonal codes over F(q)2. Then we give some newq-ary quantum codes in this case. Moreover many newq-ary quantum MDS codes with lengths of the form w(q(2)-1)/u and minimum distances d > q/2 are presented.

引用

页码：2745 / 2758

页数：14