LINEAR COMPLEMENTARY DUAL CODES AND DOUBLE CIRCULANT CODES OVER A SEMI-LOCAL RING

被引：3
|
作者：
Cheng, X. I. A. N. G. D. O. N. G. [1 ]
Cao, X. I. W. A. N. G. [1 ,2 ]
Qian, L. I. Q. I. N. [1 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut Nanjing, Sch Math, Nanjing 211106, Jiangsu, Peoples R China
[2] Key Lab Math Modelling NUAA & High Performance Com, Nanjing 211106, Jiangsu, Peoples R China
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2024年 / 18卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Cyclic code; Gray map; LCD code; LCD double circulant code; CYCLIC CODES; LCD CODES;
D O I：
10.3934/amc.2022055
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let q be an odd prime power and F-q be the finite field with q elements. In this paper, suppose ring R = F-q + mu F-q + nu F-q + mu nu F-q, where mu nu = nu mu, mu(2) =mu, nu(2) = nu. We first give a Gray map from R onto F4q and consider a decomposition of the ring R. Additionally, we investigate linear complementary dual (LCD) codes over the ring R. Some conditions for such linear codes over R to be linear complementary dual are given. Furthermore, based on the Artin conjecture, we get a class of good codes by calculating the total number of LCD double circulant codes over R.
引用
收藏
页码：1010 / 1021
页数：12
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