In this paper we consider matrix codes equipped with either the Hamming or the rank distance and study the optimal sizes of such codes with a given minimum distance. We use a maximality argument (the Gilbert-Varshamov argument) to show that, asymptotically, maximum size codes are optimal and have the same size for both rank and Hamming distances.

中文翻译：

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具有汉明距离和秩距离的渐近最优矩阵码

在本文中，我们考虑配备汉明距离或秩距离的矩阵码，并研究具有给定最小距离的此类码的最佳大小。我们用一个极大性参数（吉尔伯特- Varshamov参数）表明，渐进，最大尺寸代码是最佳的，并且具有相同的大小两个等级和汉明距离。