量子常数循环码

量子常数循环码

李卓;邢莉娟;王新梅

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

收稿日期:2007-11-12 修回日期:1900-01-01 出版日期:2009-02-20 发布日期:2009-02-10

Quantum constacyclic codes

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

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

Received:2007-11-12 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-10

摘要/Abstract

摘要： 提出了一类新的量子稳定子码的构造方法．寻找量子稳定子码的问题可以转化为寻找GF(4)上迹内积自正交的经典加码的问题．利用这一联系，提出了GF(4)上的经典常数循环码满足迹内积自正交的充要条件，从而构造出了对应的量子常数循环码．最后给出了该类码的一些例子，特别是利用该方法可以构造出量子汉明码．常见的量子循环码实际上是量子常数循环码的一个子类．

关键词: 量子常数循环码, 量子稳定子码, GF(4)上常数循环码, 量子汉明码

Abstract: A new class of quantum stabilizer codes is presented. The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Based on this connection, one method for constructing quantum constacyclic codes is presented by finding self-orthogonal classical constacyclic codes over the field GF(4) under a trace inner product. Finally, some examples are given. As an application of this method, quantum Hamming codes are constructed. This class of quantum codes includes well-known quantum cyclic codes.

Key words: quantum constacyclic codes, stabilizer quantum-error-correcting codes, constacyclic codes over GF(4), quantum Hamming codes

中图分类号:

TN911.2

李卓;邢莉娟;王新梅. 量子常数循环码
[J]. J4, 2009, 36(1): 48-51.

LI Zhuo;XING Li-juan;WANG Xin-mei. Quantum constacyclic codes
[J]. J4, 2009, 36(1): 48-51.

[1]	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.
[2]	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.
[3]	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.