一类量子重根循环码的构造  

Construction of a Class of Quantum Repeated-Root Cyclic Codes

作　　者：王艳萍 晋守博[1] 李杰[1] 费时龙[1] 高凤伟[1] WANG Yanping;JIN Shoubo;LI Jie;FEI Shilong;GAO Fengwei(Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《通化师范学院学报》2024年第12期31-37,共7页Journal of Tonghua Normal University

基　　金：安徽省高校自然科学研究项目(2022AH040207,KJ2021A1102,2024AH040374);安徽省社科创新发展项目(2023CX511);宿州学院重点科研项目(2024yzd19);宿州学院横向项目(2024xhx053,2024xhx073,2024xhx181);宿州学院教学创新团队(szxy2023cxtd01);宿州学院质量工程项目(szxy2023jhxm02);宿州学院科研发展基金项目(2021fzjj15);宿州学院教学研究项目(szxy2024jyxm19,szxy2023jyxm37);安徽省青年骨干教师境内访学研修资助项目(JNFX2024066,JNFX2023066);教育部协同育人项目(220802148255702)。

摘　　要：为了拓展量子纠错码的结构,提高其在量子计算中的纠错能力和编码效率,文章构造了一类新的量子重根循环码.首先研究了Fq上码长为6ps重根循环码包含对偶码的充要条件;其次,基于其最小汉明距离,给出对偶包含码的汉明距离;最后,根据重根循环码的代数结构,借助Steane扩展构造,给出了几类不同参数的量子码.通过精确控制码参数,提升了量子纠错码在量子通信中的实用性和可靠性.In order to expand the structure of quantum error-correcting codes and improve their errorcorrecting ability and coding efficiency in quantum computing,a new class of quantum repeated-root cyclic codes is constructed.In this paper,firstly,the sufficient and necessary conditions for the repeatedroot cyclic codes of length 6ps over Fq containing dual codes are studied.Secondly,based on its minimum Hamming distance,the Hamming distance of dual inclusion code is given.Finally,several kinds of quantum codes with different parameters are given based on the algebraic structure of repeated-root cyclic codes and Steane's enlargement construction.The practicability and reliability of quantum error-correcting codes in quantum communication are improved by precisely controlling code parameters.

关 键 词：量子码 对偶码 汉明距离 循环码 

分 类 号：O157.4[理学—数学]