Quasi-Cyclic Codes of Index 1 1/3

被引：22

作者：

Fan, Yun ^{[1
]}

Liu, Hualu ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2016年 / 62卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Quasi-cyclic code; fractional index; relative minimum distance; random code; asymptotically good code; ASYMPTOTICALLY GOOD;

D O I：

10.1109/TIT.2016.2602842

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We introduce quasi-cyclic codes of index 1(1/3), and construct a class of such codes generated by pairs of polynomials. By investigating the pair of circulant matrices associated with the generator pair of polynomials, we obtain the generator matrix of any code of the class. Using a probabilistic method, we prove that, for any positive real number delta such that the asymptotic GV-bound at 2 delta is greater than 1/2, the probability that the relative minimal distance of the code in the class is greater than d is almost 1; and the probability that the rate of the code equals to 1/4 is also almost 1. An obvious consequence is that the quasicyclic codes of index 1(1/3) are asymptotically good.

引用

页码：6342 / 6347

页数：6