Título:
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Cycle codes of graphs and MDS array codes
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Autor/a:
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Serra Albó, Oriol; Zemor, Gilles
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
Abstract:
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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. |
Abstract:
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Peer Reviewed |
Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria -Graph theory -Grafs, Teoria de -05C Graph theory |
Derechos:
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Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento:
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Artículo - Versión publicada Artículo |
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