# 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…
9 Citations
Explicit symmetric pseudo-random matrices
• Computer Science, Mathematics
2017 IEEE Information Theory Workshop (ITW)
• 2017
Using binary m-sequences (Golomb sequences) of lengths n, a simple explicit construction of circulant n × n sign matrices is given and it is shown that their spectra converge to the semicircular law when n grows.
RANDOM MATRICES FROM LINEAR CODES AND THE CONVERGENCE TO WIGNER ’ S SEMICIRCLE LAW
• Computer Science
• 2019
It is shown that the dual distance being at least 5 is sufficient to ensure the convergence, and the convergence rate is of the form n−β for some 0 < β < 1, where n is the length of the code.
Random Matrices From Linear Codes and Wigner’s Semicircle Law
• Computer Science, Mathematics
IEEE Transactions on Information Theory
• 2019
In this paper, we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions
Random Matrices from Linear Codes and Wigner’s Semicircle Law II
• Computer Science
2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA)
• 2019
By employing more advanced techniques related to Stieltjes transform, it is shown that the dual distance being at least 5 is sufficient to ensure the convergence and a fast convergence rate in terms of the length of the code is obtained.
Asymptotically Pseudo-Independent Matrices
• Mathematics, Computer Science
• 2018
We show that the family of pseudo-random matrices recently discovered by Soloveychik, Xiang, and Tarokh in their work `Symmetric Pseudo-Random Matrices' exhibits asymptotic independence. More
Spectral distribution of random matrices from Mutually Unbiased Bases.
• Mathematics, Computer Science
• 2019
We consider the random matrix obtained by picking vectors randomly from a large collection of mutually unbiased bases of $\mathbb{C}^n$, and prove that the spectral distribution converges to the
On the Complete Weight Distribution of Subfield Subcodes of Algebraic-Geometric Codes
• Computer Science
IEEE Transactions on Information Theory
• 2019
A large family of subfield subcodes of algebraic-geometric codes over prime fields which include BCH codes and Goppa codes are considered and it is proved that the complete weight distribution is close to that of a random code if the code length is large compared with the genus of the curve and the degree of the divisor defining the code.
Kesten–McKay Law for Random Subensembles of Paley Equiangular Tight Frames
• Mathematics
ArXiv
• 2019
The method of moments is applied to prove a recent conjecture of Haikin, Zamir and Gavish concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames to prove that this conjecture is true.