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Cycle codes of graphs and MDS array codes
dc.contributor.author | Serra Albó, Oriol |
dc.contributor.author | Zemor, Gilles |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2010-03-22T10:33:50Z |
dc.date.available | 2010-03-22T10:33:50Z |
dc.date.created | 2009-07-30 |
dc.date.issued | 2009-07-30 |
dc.identifier.citation | Serra, O.; Zemor, G. Cycle codes of graphs and MDS array codes. "Electronic notes in discrete mathematics", 30 Juliol 2009, núm. 34, p. 95-99. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/6739 |
dc.description.abstract | We investigate how to colour edges of graph so that any two colours make up a spanning tree. This problem is equivalent to transforming the cycle code of a graph into a Maximum Distance Separable (MDS) array code. Adopting this graph-theoretical interpretation allows us to provide a compact description of some families of low density MDS array codes in terms of cycle codes of coloured graphs. This includes a short description of Xu et al.’s “B-code”, together with its erasure and error decoding algorithms. We also give a partial answer to Xu et al.’s question about efficient error decoding for the dual B-code. We give alternative families of MDS array cycle codes, and in passing prove that an optimal MDS array cycle code of minimum column distance 4 is given by an appropriate colouring of the Petersen graph. We introduce double array colourings which allow the decoding of column or row errors and provides a new interesting graph theoretical problem. We give infinite families of graphs which admit double array colourings. |
dc.format.extent | 5 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
dc.subject.lcsh | Graph theory |
dc.title | Cycle codes of graphs and MDS array codes |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1016/j.endm.2009.07.016 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | 05C Graph theory |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 2099661 |
dc.description.version | Postprint (published version) |
local.citation.author | Serra, O.; Zemor, G. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.number | 34 |
local.citation.startingPage | 95 |
local.citation.endingPage | 99 |
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