一类有限链环上的厄米特自正交码  

Hermite Self-orthogonal Codes over a Class of Finite Chain Ring

作　　者：钟家伟 ZHONG Jiawei(College of General Education and Foreign Languages,Anhui Institute of Information Technology,Wuhu 241000,China)

机构地区：[1]安徽信息工程学院通识教育与外国语学院,安徽芜湖241000

出　　处：《长春大学学报》2022年第4期28-31,共4页Journal of Changchun University

基　　金：安徽省教育厅高校自然科学重点项目(KJ2019A1286)

摘　　要：随着量子通信和量子计算技术的不断发展,构造具有最大距离可分量子码(简记为MDS量子码)成为量子编码理论的研究重点。由于量子码可以通过自正交码进行构造的特点,近年来构造了许多具有良好参数的自正交码。通过所定义的有限链环F_(q)+uF_(q)上的齐次重量,构造环F_(q)+uF_(q)上的齐次距离到q元域上的汉明距离的广义Gray映射,并证明了其为保距映射。通过q元域上两类厄米特自正交码构造了环F_(q)+uF_(q)上厄米特自正交码,最后举例说明。With the development of the technologies of quantum communication and quantum computing,the construction of maximum distance divisible quantum codes(MDS quantum codes)becomes the focus of quantum coding theory.Since quantum codes can be constructed by self-orthogonal codes,many self-orthogonal codes with good parameters have been constructed in recent years.Generalized Gray map is constructed from the homogeneous distance over ring F_(q)+uF_(q)to the hamming distance over q elements field by the homogeneous weight over finite chain ring F_(q)+uF_(q),and that it is a distance-preserving map is proved.Hermite self-orthogonal codes over ring F_(q)+uF_(q)are constructed by two kinds of Hermite self-orthogonal codes over q elements field,and examples are given to illustrate them.

关 键 词：厄米特自正交码 量子码 齐次距离 广义Gray映射 极小距离 

分 类 号：O413[理学—理论物理]