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.

翻译：本研究探讨了厄米特秩度量码——秩度量码的一个特殊子类，重点关注完美码及其覆盖性质的分析。首先，我们建立了厄米特矩阵空间中球体大小的界，并由此证明在厄米特情形下不存在非平凡完美码。最后，我们通过分析其覆盖密度来结束本文。