对偶距离为5的极大自正交码及其子码

计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (17): 45-49.

对偶距离为5的极大自正交码及其子码

贺筱军¹，赵学军^1,2，李瑞虎¹，郭罗斌¹

1.空军工程大学理学院数理系，西安 710051
2.空军工程大学导弹学院，陕西三原 713800

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-06-11 发布日期:2007-06-11
通讯作者: 贺筱军

Binary minimum self-orthogonal codes of dual distance five and their subcodes

HE Xiao-jun¹，ZHAO Xue-jun^1,2，LI Rui-hu¹，GUO Luo-bin¹

1.College of Science，Air Force Engineering University，Xi’an 710051，China
2.Institute of Missile，Air Force Engineering University，Sanyuan，Shaanxi 710051，China

Received:1900-01-01 Revised:1900-01-01 Online:2007-06-11 Published:2007-06-11
Contact: HE Xiao-jun

摘要/Abstract

摘要： 研究了自对偶码与其删截得到的极大自正交码的等价性问题。利用删截法构造出码长n满足21≤n≤29、对偶距离为5的二元极大自正交码。再用随机搜索算法研究了所得到的二元极大自正交码的子码，构造出它们的对偶距离为3和5的子码的生成矩阵。研究了这些子码构成的码链以及它们的对偶码构成的码链。利用所得到的码链，由Steane构造法构造出距离为5的具有很好参数的量子纠错码。

关键词: 极大自正交码, 自对偶码, S-链, 量子纠错码

Abstract: The equivalence of maximal self-orthogonal codes obtained from binary self-dual codes by truncating are discussed.Many non-equivalent maximal self-orthogonal codes of length 21≤n≤29 and dual distance five are constructed by truncating self-dual codes of dual distance six.Subcodes of these maximal self-orthogonal codes are studied by using of a random search algorithm，and the subcodes of dual distance 3 and 5 of these maximal self-orthogonal codes are constructed.The code chains of these self-orthogonal subcodes and the S-chains obtained from the dual of these self-orthogonal subcodes are also determined.According to Steane’s construction，some very good quantum codes of distance five are constructed by the obtained S-chains.

Key words: self-orthogonal codes, self-dual codes, S-chains, quantum error-correcting codes

贺筱军¹，赵学军^1,2，李瑞虎¹，郭罗斌¹. 对偶距离为5的极大自正交码及其子码[J]. 计算机工程与应用, 2007, 43(17): 45-49.

HE Xiao-jun¹，ZHAO Xue-jun^1,2，LI Rui-hu¹，GUO Luo-bin¹. Binary minimum self-orthogonal codes of dual distance five and their subcodes[J]. Computer Engineering and Applications, 2007, 43(17): 45-49.

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