Quotients of Gaussian graphs and their application to perfect codes
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 wi...
| Autores: | , , , , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2010 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositório: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.unican.es:10902/39298 |
| Acesso em linha: | https://hdl.handle.net/10902/39298 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Gaussian integers Perfect codes Lee metric Codes on graphs |
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Quotients of Gaussian graphs and their application to perfect codesMartínez Fernández, María del Carmen|||0000-0002-9815-239XBeivide Palacio, Ramón|||0000-0002-9591-7078Camarero Coterillo, Cristóbal|||0000-0001-6418-2614Stafford Fernández, Esteban|||0000-0001-9481-8724 Gabidulin, E.M.Gaussian integersPerfect codesLee metricCodes on graphsA 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.The authors would like to thank the Editor and the anonymous referees for their careful reading of the paper and useful suggestions. The work of C. Martínez and R. Beivide was supported by the Spanish Ministry of Education and Science under Contract TIN2007-68023-C02-01, CONSOLIDER Project CSD2007-00050, the European Network of Excellence on High-Performance and Embedded Architecture and Compilation, and by the Research Programme of the University of Cantabria under Contract 030.VI16.648.ElsevierUniversidad de Cantabria20102010-07-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/39298Journal of Symbolic Computation, 2010, 45(7), 813-824reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/392982026-06-02T12:39:31Z |
| dc.title.none.fl_str_mv |
Quotients of Gaussian graphs and their application to perfect codes |
| title |
Quotients of Gaussian graphs and their application to perfect codes |
| spellingShingle |
Quotients of Gaussian graphs and their application to perfect codes Martínez Fernández, María del Carmen|||0000-0002-9815-239X Gaussian integers Perfect codes Lee metric Codes on graphs |
| title_short |
Quotients of Gaussian graphs and their application to perfect codes |
| title_full |
Quotients of Gaussian graphs and their application to perfect codes |
| title_fullStr |
Quotients of Gaussian graphs and their application to perfect codes |
| title_full_unstemmed |
Quotients of Gaussian graphs and their application to perfect codes |
| title_sort |
Quotients of Gaussian graphs and their application to perfect codes |
| dc.creator.none.fl_str_mv |
Martínez Fernández, María del Carmen|||0000-0002-9815-239X Beivide Palacio, Ramón|||0000-0002-9591-7078 Camarero Coterillo, Cristóbal|||0000-0001-6418-2614 Stafford Fernández, Esteban|||0000-0001-9481-8724 Gabidulin, E.M. |
| author |
Martínez Fernández, María del Carmen|||0000-0002-9815-239X |
| author_facet |
Martínez Fernández, María del Carmen|||0000-0002-9815-239X Beivide Palacio, Ramón|||0000-0002-9591-7078 Camarero Coterillo, Cristóbal|||0000-0001-6418-2614 Stafford Fernández, Esteban|||0000-0001-9481-8724 Gabidulin, E.M. |
| author_role |
author |
| author2 |
Beivide Palacio, Ramón|||0000-0002-9591-7078 Camarero Coterillo, Cristóbal|||0000-0001-6418-2614 Stafford Fernández, Esteban|||0000-0001-9481-8724 Gabidulin, E.M. |
| author2_role |
author author author author |
| dc.contributor.none.fl_str_mv |
Universidad de Cantabria |
| dc.subject.none.fl_str_mv |
Gaussian integers Perfect codes Lee metric Codes on graphs |
| topic |
Gaussian integers Perfect codes Lee metric Codes on graphs |
| description |
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. |
| publishDate |
2010 |
| dc.date.none.fl_str_mv |
2010 2010-07-01 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 NA http://purl.org/coar/version/c_be7fb7dd8ff6fe43 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/10902/39298 |
| url |
https://hdl.handle.net/10902/39298 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.publisher.none.fl_str_mv |
Elsevier |
| publisher.none.fl_str_mv |
Elsevier |
| dc.source.none.fl_str_mv |
Journal of Symbolic Computation, 2010, 45(7), 813-824 reponame:UCrea Repositorio Abierto de la Universidad de Cantabria instname:Universidad de Cantabria (UC) |
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Universidad de Cantabria (UC) |
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UCrea Repositorio Abierto de la Universidad de Cantabria |
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UCrea Repositorio Abierto de la Universidad de Cantabria |
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1869407610866761728 |
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15,812429 |