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

Chin Hei Chan; Vahid Tarokh; Maosheng Xiong

doi:10.1109/tit.2020.3039175

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arXiv · 1902.08428

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

Chin Hei Chan·Vahid Tarokh·Maosheng Xiong

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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.

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Chin Hei Chan, Vahid Tarokh, Maosheng Xiong. 2019-02-22. Convergence Rate of Empirical Spectral Distribution of Random Matrices from Linear Codes. https://doi.org/10.1109/tit.2020.3039175

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