|
Title:
|
Cycle codes of graphs and MDS array codes
|
|
Author:
|
Serra Albó, Oriol; Zemor, Gilles
|
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
|
Abstract:
|
We investigate how to colour edges of graph so that any two colours make upa spanning tree. This problem is equivalent to transforming the cycle code ofa graph into a Maximum Distance Separable (MDS) array code. Adopting thisgraph-theoretical interpretation allows us to provide a compact description of somefamilies 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 erasureand error decoding algorithms. We also give a partial answer to Xu et al.’s questionabout efficient error decoding for the dual B-code. We give alternative families ofMDS array cycle codes, and in passing prove that an optimal MDS array cycle codeof minimum column distance 4 is given by an appropriate colouring of the Petersengraph. We introduce double array colourings which allow the decoding of columnor row errors and provides a new interesting graph theoretical problem. We giveinfinite families of graphs which admit double array colourings. |
|
Publication date:
|
2012-05-10 |
|
Subject(s):
|
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria Graph theory Grafs, Teoria de 05C Graph theory |
|
Rights:
|
Restricted access - publisher's policy |
|
Document type:
|
Article |
|
Share:
|
|