基于初等变换的量子码构造  

Construction of quantum codes based on elementary transformations

作　　者：陈汉武[1,2] 肖芳英[1] 

机构地区：[1]东南大学计算机科学与工程学院,南京211189 [2]东南大学计算机网络和信息集成教育部重点实验室,南京211189

出　　处：《东南大学学报（自然科学版）》2011年第5期934-937,共4页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60873101);东南大学计算机网络和信息集成教育部重点实验室开放基金资助项目

摘　　要：为了探讨一般量子稳定子码的简单构造方法,在满足对偶包含条件C⊥C的约束下,提出了从一类量子稳定子码C=[[N,K,D]]q到量子稳定子码C'=[[N-1,K+1,D']]q的基于矩阵初等变换的构造方法.该方法的优点在于码字构造时,量子稳定子码和经典纠错码都是在Fq上进行操作,无须做Fq2到Fq上的映射转换,也无须使用复杂的数学运算,仅使用内积空间和初等矩阵行变换的相关概念即可构造一类码字的衍生码,因此该构造算法可提高时空效率.另外,该方法构造性的证明简单、易懂,且易于计算机及各种硬件系统实现.研究理论结果显示,该方法对一类量子码的构造非常实用.To investigate the general technique for simply constructing quantum stabilizer code,when the conditions of the dual constraints（C⊥C） are met,a new constructing method based on elementary transformations is put forward,by which a class of quantum stabilizer codes C′=[[N-1,K＋1,D′]]q can be constructed from another class of quantum stabilizer codes C=[]q with C⊥C.In the codes structure,quantum stabilizer codes and classical error correction codes operate on the same field Fq,eliminating the conversion from Fq2 to Fq and complicated mathematical operations.Using only the concepts of inner product space and elementary row transformation matrix,a class of derivative code of the codes can be constructed,and the efficiency of time and space of the algorithm can be improved.Constructive proof of the method is simple and easy to understand.In addition,the code construction and check are easy to implement,especially applicable to computer.Theoretical results show that the method is helpful for the construction of a class of quantum codes.

关 键 词：量子纠错码 生成矩阵 奇偶校验矩阵 初等行变换 截短码 

分 类 号：TP387[自动化与计算机技术—计算机系统结构]