Properties of subspace subcodes of optimum codes in rank metric

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dc.creatorGabidulin, E. M.
dc.creatorLoidreau, P.
dc.date2006-07-25
dc.date.accessioned2026-07-07T08:16:40Z
dc.date.available2026-07-07T08:16:40Z
dc.descriptionMaximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time decoding algorithms. These codes can be seen as the analogs of Reed-Solomon codes (hereafter denoted RS-codes) for rank metric. In this paper their subspace subcodes are characterized. It is shown that hey are equivalent to MRD-codes constructed in the same way but with smaller parameters. A specific polynomial-time decoding algorithm is designed. Moreover, it is shown that the direct sum of subspace subcodes is equivalent to the direct product of MRD-codes with smaller parameters. This implies that the decoding procedure can correct errors of higher rank than the error-correcting capability. Finally it is shown that, for given parameters, subfield subcodes are completely characterized by elements of the general linear group ${GL}_n(\FF{q})$ of non-singular $q$-ary matrices of size $n$.
dc.description17 pages, Submitted to IEEE-IT
dc.identifierhttps://arxiv.org/abs/cs/0607108
dc.identifierhttp://arxiv.org/abs/cs/0607108
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133858
dc.subjectInformation Theory
dc.subjectDiscrete Mathematics
dc.titleProperties of subspace subcodes of optimum codes in rank metric
dc.typetext

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