自正交码的组合构造与应用  

Combinational Construction of Self-orthogonal Codes and Its Application

作　　者：刘乃功[1] 郭罗斌[1] 刘健[2] 

机构地区：[1]空军工程大学理学院,陕西西安710051 [2]空军工程大学导弹学院,陕西三原713800

出　　处：《空军工程大学学报（自然科学版）》2009年第1期88-90,94,共4页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60573040)

摘　　要：量子纠错码是量子计算和量子通信可靠运行的保障,构造具有很好参数的量子纠错码是重要的研究问题之一。用二元线性码构造量子码的方法有CSS(Calderbank-Shor-Steane)方法和Steane方法,这两种方法都建立在如何构造给定对偶距离的自正交码上,研究了用组合方法构造二元自正交码问题。由已知对偶距离的二元自正交码链,用组合方法构造对偶距离为3、4、5和6的二元自正交码,以及对偶距离为3、4、5和6的二元自正交码构成二元自正交码链的条件。在此基础上,对每个满足47≤n≤70的,构造出参数为[n,n-s-t,5]■[n,n-s,3]和[n,n-u-v,6]■[n,n-v,4]的S-链。利用所得到的码链,由Steane构造法构造出距离为5和6的具有很好参数的量子纠错码,改进了前人得到的几个量子纠错码的参数。Quantum error - correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication. It is one of important problems that constructing very good quantum codes. There are two methods that use binary codes to construct quantum codes,one is CSS construction, another is Steane construction. These two methods are all based on the construction of binary self - orthogonal codes. Combinational construction of binary self - orthogonal codes is investigated in this paper. From known codes chains of binary self - orthogonal codes and their dual codes chains with given dual distance, new binary self - orthogonal codes of dual distance three, four, five and six are constructed. Based on these results, for each satisfying , S - chains with parameters and are constructed. According to Steane＇s construction, many very good quantum codes of distance five and six are constructed by the obtained S - chains, some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.

关 键 词：自正交码 S-链 量子纠错码 

分 类 号：O157.4[理学—数学]