Constant-Rank Codes

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dc.creatorGadouleau, Maximilien
dc.creatorYan, Zhiyuan
dc.date2008-03-06
dc.date2008-05-07
dc.date.accessioned2026-07-07T09:37:12Z
dc.date.available2026-07-07T09:37:12Z
dc.descriptionConstant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant-rank codes are closely related to constant-dimension codes and we study the properties of constant-rank codes. We first introduce a relation between vectors in $\mathrm{GF}(q^m)^n$ and subspaces of $\mathrm{GF}(q)^m$ or $\mathrm{GF}(q)^n$, and use it to establish a relation between constant-rank codes and constant-dimension codes. We then derive bounds on the maximum cardinality of constant-rank codes with given rank weight and minimum rank distance. Finally, we investigate the asymptotic behavior of the maximal cardinality of constant-rank codes with given rank weight and minimum rank distance.
dc.description5 pages, to appear in Proc. IEEE ISIT 2008
dc.identifierhttps://arxiv.org/abs/0803.0778
dc.identifierhttp://arxiv.org/abs/0803.0778
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160375
dc.subjectInformation Theory
dc.titleConstant-Rank Codes
dc.typetext

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