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

页码：1010 / 1021

页数：12

共 20 条

[1] COMPLEMENTARY DUAL CODES FOR COUNTER-MEASURES TO SIDE-CHANNEL ATTACKS [J].