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arXiv · 2409.16753

Perfect Hermitian rank-metric codes

Usman Mushrraf
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Abstract

This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of Hermitian matrices and, as a consequence, we show that non-trivial perfect codes do not exist in the Hermitian case. We conclude the paper by examining their covering density.

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Usman Mushrraf. 2025-08-06. Perfect Hermitian rank-metric codes. https://arxiv.org/abs/2409.16753

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