Perfect Hermitian rank-metric codes
Usman Mushrraf
TL;DR
This paper explores Hermitian rank-metric codes, establishing bounds and proving the non-existence of non-trivial perfect codes, while analyzing their covering properties and density.
Contribution
It provides new bounds on sphere sizes in Hermitian matrix spaces and proves that non-trivial perfect codes do not exist in this setting.
Findings
Non-trivial perfect Hermitian rank-metric codes do not exist.
Established bounds on sphere sizes in Hermitian matrix spaces.
Analyzed covering density of Hermitian rank-metric codes.
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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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Advanced Wireless Network Optimization