一类量子重根循环码的构造
Construction of a Class of Quantum Repeated-Root Cyclic Codes
王艳萍 1晋守博 1李杰 1费时龙 1高凤伟1
作者信息
- 1. 宿州学院数学与统计学院(安徽 宿州 234000)
- 折叠
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.
Abstract
In order to expand the structure of quantum error-correcting codes and improve their error-correcting 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 repeated-root 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 quan-tum 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Key words
quantum codes/dual codes/Hamming distance/cyclic codes引用本文复制引用
出版年
2024
NETL
NSTL
万方数据