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

Probability 2021-02-01 v4 Information Theory math.IT

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 n1/4n^{-1/4} where nn is the length of the code.

Keywords

Cite

@article{arxiv.1902.08428,
  title  = {Convergence Rate of Empirical Spectral Distribution of Random Matrices from Linear Codes},
  author = {Chin Hei Chan and Vahid Tarokh and Maosheng Xiong},
  journal= {arXiv preprint arXiv:1902.08428},
  year   = {2021}
}