A modified Gilbert-Varshamov bound for self-dual quasi-twisted codes of index four

被引：16
|
作者：
Wu, Rongsheng [1 ,2 ]
Shi, Minjia [1 ,2 ]
机构：
[1] Anhui Univ, Sch Math Sci, Key Lab Intelligent Comp Signal Proc, Hefei 230601, Anhui, Peoples R China
[2] Anhui Univ, Sch Math Sci, Minist Educ, Hefei 230601, Anhui, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2020年 / 62卷
基金：
中国国家自然科学基金;
关键词：
Self-dual codes; Four circulant codes; Four negacirculant codes; Artin's primitive root conjecture; Gilbert-Varshamov bound; CYCLIC CODES;
D O I：
10.1016/j.ffa.2019.101627
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we study a family of self-dual four circulant codes and a family of self-dual four negacirculant codes, and the exact counting formula is derived for these families of codes. In addition, we prove that asymptotically good self-dual four circulant codes and negacirculant codes over finite fields exist, and both of them satisfy a modified Gilbert-Varshamov bound on the relative minimum distance with asymptotic rate 1/2. (C) 2019 Elsevier Inc. All rights reserved.
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页数：11
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