Explicit symmetric pseudo-random matrices

Conference Paper

We consider the problem of generating symmetric pseudo-random sign (±1) matrices based on the similarity of their spectra to Wigner's semicircular law. Using binary m-sequences (Golomb sequences) of lengths n = 2m - 1, we give a simple explicit construction of circulant n × n sign matrices and show that their spectra converge to the semicircular law when n grows. The Kolmogorov complexity of the proposed matrices equals to that of Golomb sequences and is at most 2log2(n) bits.

Full Text

Duke Authors

Cited Authors

  • Soloveychik, I; Xiang, Y; Tarokh, V

Published Date

  • January 31, 2018

Published In

Volume / Issue

  • 2018-January /

Start / End Page

  • 424 - 428

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781509030972

Digital Object Identifier (DOI)

  • 10.1109/ITW.2017.8277999

Citation Source

  • Scopus