Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams

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dc.creatorEtzion, Tuvi
dc.creatorSilberstein, Natalia
dc.date2008-07-30
dc.date2009-03-14
dc.date.accessioned2026-07-07T12:52:02Z
dc.date.available2026-07-07T12:52:02Z
dc.descriptionCoding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the projective space. In this paper we propose a method to design error-correcting codes in the projective space. We use a multilevel approach to design our codes. First, we select a constant weight code. Each codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric code. Each such rank-metric code is lifted to a constant dimension code. The union of these codes is our final constant dimension code. In particular the codes constructed recently by Koetter and Kschischang are a subset of our codes. The rank-metric codes used for this construction form a new class of rank-metric codes. We present a decoding algorithm to the constructed codes in the projective space. The efficiency of the decoding depends on the efficiency of the decoding for the constant weight codes and the rank-metric codes. Finally, we use puncturing on our final constant dimension codes to obtain large codes in the projective space which are not constant dimension.
dc.descriptionRevised for IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/0807.4846
dc.identifierhttp://arxiv.org/abs/0807.4846
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223176
dc.subjectInformation Theory
dc.titleError-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams
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