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
收藏
页码：162 / 176
页数：15
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