2018/10/31 by Zhangchi Chen · 1 citation
Mathematics · #math.AC #msc:15B05 #msc:11R18 #msc:68P30 #msc:94A05
paper · pdf · doi:10.1016/j.laa.2020.12.010
published as Linear Algebra and its Applications Volume 612, 1 March 2021, Pages 162-176 · 12 pages. To be published in Linear Algebra and Its Applications
arxiv created 2020/12/08 · arxiv updated 2020/12/21
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.