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Quotients of Gaussian graphs and their application to perfect codes

Abstract: A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.

 Autoría: Martínez C., Beivide R., Camarero C., Stafford E., Gabidulin E.,

 Fuente: Journal of Symbolic Computation, 2010, 45(7), 813-824

 Editorial: Elsevier

 Fecha de publicación: 01/07/2010

 Nº de páginas: 12

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jsc.2010.03.013

 ISSN: 0747-7171,1095-855X

 Proyecto español: TIN2007-68023-C02-01

 Url de la publicación: https://doi.org/10.1016/j.jsc.2010.03.013