期刊
LINEAR ALGEBRA AND ITS APPLICATIONS
卷 612, 期 -, 页码 162-176出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2020.12.010
关键词
Circulant matrices; Cyclotomic polynomials; Communication theory; Coding
This study demonstrates that specific circulant matrices with k ones and k + 1 zeros in the first row are always nonsingular under certain conditions, but may become singular for other integer cases. The smallest singular matrix appears when 2k + 1 = 45, with the possibility of such matrices being singular being less than 10^(-4).
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.
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