Properties of Codes with the Rank Metric

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dc.creatorGadouleau, Maximilien
dc.creatorYan, Zhiyuan
dc.date2006-10-16
dc.date2006-10-25
dc.date.accessioned2026-07-07T08:16:46Z
dc.date.available2026-07-07T08:16:46Z
dc.descriptionIn this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD codes and sphere-packing bound cannot be attained. We also establish bounds on the rank covering radius of maximal codes, and show that all MRD codes are maximal codes and all the MRD codes known so far achieve the maximum rank covering radius.
dc.description5 pages, 4 figures, accepted to Globecom 2006
dc.identifierhttps://arxiv.org/abs/cs/0610099
dc.identifierhttp://arxiv.org/abs/cs/0610099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133893
dc.subjectInformation Theory
dc.titleProperties of Codes with the Rank Metric
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