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Perfect Hermitian rank-metric codes

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arxiv 2409.16753 v2 pith:H6QUDAWW submitted 2024-09-25 cs.IT math.IT

Usman Mushrraf This is my paper · ORCID
classification cs.ITmath.IT
keywords codeshermitianperfectrank-metriccoveringanalysisboundscase
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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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  1. On the non-existence of perfect codes in the sum-rank metric

    cs.IT 2025-08 conditional novelty 6.0 of 10

    Perfect codes in the sum-rank metric are shown to be impossible for large families of parameters, though the two-block case for small radius and q>e^3 is left unresolved by the proof.

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