Convergence Rate of Empirical Spectral Distribution of Random Matrices From Linear Codes

Abstract

It is known that the empirical spectral distribution of random matrices obtained from linear codes of increasing length converges to the well-known Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5. In this paper, we prove that the convergence in probability is at least of the order $n^{-1/4}$ where $n$ is the length of the code.