Random Matrices from Linear Codes and Wigner's semicircle law
Information Theory
2018-08-29 v1 Discrete Mathematics
math.IT
Abstract
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 of the codes their empirical spectral distribution converges to Wigner's semicircle law as the length of the codes goes to infinity. One such condition is that the dual distance of the codes is at least 5. This is analogous to previous work on the empirical spectral distribution of similar matrices obtained in this fashion that converges to the Marchenko-Pastur law.
Cite
@article{arxiv.1808.09129,
title = {Random Matrices from Linear Codes and Wigner's semicircle law},
author = {Chin Hei Chan and Enoch Kung and Maosheng Xiong},
journal= {arXiv preprint arXiv:1808.09129},
year = {2018}
}