一类量子循环码的构造方法

一类量子循环码的构造方法

李卓;邢莉娟;王新梅

(西安电子科技大学综合业务网理论与关键技术国家重点实验室，陕西西安 710071)

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-04-20 发布日期:2007-04-20

A construction method for a family of quantum cyclic codes

LI Zhuo;XING Li-juan;WANG Xin-mei

(State Key Lab. of Integrated Service Networks, Xidian Univ., Xi′an 710071， China)

Received:1900-01-01 Revised:1900-01-01 Online:2007-04-20 Published:2007-04-20

摘要/Abstract

摘要： 寻找量子稳定子码的问题可以转化为寻找GF(4)上厄米内积自正交的经典线性码的问题;对于GF(4)上的经典循环码，它是厄米内积自正交的，当且仅当它的对偶码的生成多项式是其生成多项式的因子．利用这一关系，通过寻找生成多项式满足该条件的经典循环码，构造出一类量子循环码，并详细给出了该类码的一些例子．

关键词: 量子循环码, 量子稳定子码, GF(4)上循环码, 厄米内积, 自正交

Abstract: The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding classical self-orthogonal linear codes over the Galois field GF(4) under a Hermitian inner product. A classical cyclic code over the field GF(4) is self-orthogonal with respect to the Hermitian inner product iff the generator polynomial of its dual code is a factor of its generator polynomial. Based on this connection, a class of quantum cyclic codes is constructed by finding corresponding classical cyclic codes. Some examples are also given in detail.

Key words: quantum cyclic codes, stabilizer quantum-error-correcting codes, cyclic codes over the field GF(4), Hermitian inner product, self-orthogonal

中图分类号:

TN911.2

李卓;邢莉娟;王新梅. 一类量子循环码的构造方法
[J]. J4, 2007, 34(2): 187-189.

LI Zhuo;XING Li-juan;WANG Xin-mei. A construction method for a family of quantum cyclic codes
[J]. J4, 2007, 34(2): 187-189.

[1]	李卓;邢莉娟;王新梅. 量子常数循环码 [J]. J4, 2009, 36(1): 48-51.
[2]	李卓;邢莉娟;王新梅. 一类量子稳定子码的编译码方法 [J]. J4, 2008, 35(5): 834-837.
[3]	邢莉娟;李卓;王新梅. 一类基于经典卷积码的量子稳定子码 [J]. J4, 2008, 35(2): 277-281.