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 rate in probability is at least of the order $n^{-1/4}$ where $n$ is the length of the code.

中文翻译：

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线性码随机矩阵经验谱分布的收敛率

已知，如果对偶码的汉明距离至少为 5，则由递增长度的线性码获得的随机矩阵的经验谱分布收敛于众所周知的马尔琴科-帕斯图定律。 在本文中，我们证明了概率收敛速度至少为 $n^{-1/4}$ 在哪里 $n$ 是代码的长度。