# Symmetric Pseudo-Random Matrices

@article{Soloveychik2018SymmetricPM,
title={Symmetric Pseudo-Random Matrices},
author={Ilya Soloveychik and Yu Xiang and Vahid Tarokh},
journal={IEEE Transactions on Information Theory},
year={2018},
volume={64},
pages={3179-3196}
}
• Published 14 February 2017
• Computer Science
• IEEE Transactions on Information Theory
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 <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>-sequences (Golomb sequences) of lengths <inline-formula> <tex-math notation="LaTeX">$n=2^{m}-1$ </tex-math></inline-formula>, we give a simple explicit construction of circulant <inline-formula> <tex-math notation="LaTeX">$n \times n$ </tex-math></inline…
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