Pseudo-wigner matrices from dual BCH codes

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. We introduce r-independent pseudo-Wigner ensembles and prove closeness of their spectra to the semicircular density in Kolmogorov distance. We give an explicit construction of a family of N × N pseudo-Wigner ensembles using dual BCH codes and show that the Kolmogorov complexity of the obtained matrices is of the order of log (N) bits for a fixed Kolmogorov distance precision. Finally, we provide numerical simulations verifying our theoretical results.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • August 9, 2017

Published In

Start / End Page

  • 1381 - 1385

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781509040964

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2017.8006755

Citation Source

  • Scopus