循环码的像构造 2 类新量子码

郭宏哲，朱士信

(合肥工业大学数学学院，安徽合肥230601)

摘要

文章给出2类循环码的像是厄米特自正交码的充分条件;对得到的2类厄米特自正交码,使用厄米特构造方法得到2类新的量子码;2类新量子码与同长度已有量子码对比,有更大的最小距离或更高的码率。

关键词

量子纠错码；循环码；厄米特自正交；厄米特构造

中图分类号：TN911.22

文献标志码：A

文章编号：1003-5060（2023）05-0704-05

Two new classes of quantum codes derived from images of cyclic codes

GUO Hongzhe, ZHU Shixin

(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract

In this paper, sufficient conditions for the images of two classes of cyclic codes to be Hermitian self-orthogonal are given. Two new classes of quantum codes are obtained from the Hermitian self-orthogonal image of cyclic codes by using Hermitian construction. These new quantum codes obtained have better parameters than the known ones with same lengths such as larger minimum distance or higher code rate.

Keywords

quantum error-correcting codes; cyclic codes; Hermitian self-orthogonal; Hermitian construction

收稿日期：2022-03-15

修回日期：2022-04-20

基金项目：国家自然科学基金资助项目（61772168；61972126；12001002；62002093）；安徽省自然科学基金资助项目（80808QA04）