On nonsingularity of circulant matrices

被引：6

作者：

Chen, Zhangchi

机构：

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 612卷

关键词：

Circulant matrices; Cyclotomic polynomials; Communication theory; Coding;

D O I：

10.1016/j.laa.2020.12.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In Communication theory and Coding, it is expected that certain circulant matrices having k ones and k + 1 zeros in the first row are nonsingular. We prove that such matrices are always nonsingular when 2k + 1 is either a power of a prime, or a product of two distinct primes. For any other integer 2k + 1 we construct circulant matrices having determinant 0. The smallest singular matrix appears when 2k + 1 = 45. The possibility for such matrices to be singular is rather low, smaller than 10(-4) in this case. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：162 / 176

页数：15