四元域上一类厄米特互补对偶常循环码

孙世林，刘丽

（合肥工业大学数学学院，安徽合肥230601）

摘要

有限域上线性互补对偶码(linear codes with complementary duals, LCD)具有良好的结构和性质,并在双用户加法器信道中得到广泛的应用。文章构造四元厄米特 LCD 常循环码,分析它们的参数,并确定其维数,给出它们最小距离的下界。

关键词

线性互补对偶码；常循环码；生成多项式

中图分类号：TN911.22

文献标志码：A

文章编号：1003-5060（2023）01-0136-05

A class of quaternary Hermitian LCD constacyclic codes

SUN Shilin, LIU Li

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

Abstract

Linear codes with complementary duals (LCD) over finite fields have good structure and properties, and are widely used in two-user adder channels. In this paper, the quaternary Hermitian LCD constacyclic codes are constructed and their parameters are analyzed. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented.

Keywords

linear codes with complementary duals(LCD); constacyclic codes; generator polynomial

收稿日期：2021-06-21

修回日期：2021-09-06

基金项目：国家自然科学基金资助项目（61972126）；中央高校基本科研业务费专项资金资助项目（PA2019GDZC0097）