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

• 学术探讨 • 上一篇    下一篇

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. 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-jun1,2,LI Rui-hu1,GUO Luo-bin1   

  1. 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: 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