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

DOI10.1109/TIT.2020.3039175zbMATH Open1465.60007arXiv1902.08428OpenAlexW2921468067MaRDI QIDQ4963952

Chin Hei Chan, Vahid Tarokh, Maosheng Xiong

Publication date: 24 February 2021

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1902.08428

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Linear codes (general theory) (94B05)

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