一种2^(m)元域上量子纠错码的构造方法  

A Construction Method of Quantum Error-correcting Codes over F_(2m)

作　　者：王玉[1] 开晓山[2] 朱士信[2] WANG Yu;KAI Xiaoshan;ZHU Shixin(School of Artificial Intelligence and Big Data,Hefei University,Hefei 230601,China;School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥学院人工智能与大数据学院,合肥230601 [2]合肥工业大学数学学院,合肥230601

出　　处：《电子与信息学报》2023年第5期1731-1736,共6页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(12171134,U21A20428);安徽省高校优秀青年人才支持计划项目(gxyqZD2021137)。

摘　　要：构造具有良好参数的量子码是量子纠错码研究的重要内容。该文利用有限非链环R=F_(4m)+vF_(4m)上的厄米特对偶包含常循环码来构造2^(m)元量子码。定义了一种新的Gray映射φ,能够将环R上线性码C的厄米特对偶包含性保持到φ(C)上。研究了环R上常循环码是厄米特对偶包含码的条件。给出了一种构造2m元量子码的方法,并构造了一些新的4元和8元量子码。Constructing quantum codes with good parameters is an important part of quantum error-correcting codes research.In this paper,2^(m)-ary quantum codes are derived through Hermitian dual-containing constacyclic codes over finite non-chain ring R=F_(4m)+vF_(4m).A new Gray mapφis defined,which is Hermitian dual-containing preserving from a linear code C over R toφ(C).The condition for constacyclic codes over R to be Hermitian dual-containing is studied.A method of constructing 2^(m)-ary quantum codes is presented,and some new 4-ary and 8-ary quantum codes are obtained.

关 键 词：常循环码 量子码 有限非链环 GRAY映射 

分 类 号：TN911.22[电子电信—通信与信息系统]