Quasi-Perfect Codes From Cayley Graphs Over Integer Rings

dc.creatorQueiroz, CQ
dc.creatorCamarero, C
dc.creatorMartinez, C
dc.creatorPalazzo, R
dc.date2013
dc.dateSEP
dc.date2014-07-30T14:19:11Z
dc.date2015-11-26T17:38:20Z
dc.date2014-07-30T14:19:11Z
dc.date2015-11-26T17:38:20Z
dc.date.accessioned2018-03-29T00:19:58Z
dc.date.available2018-03-29T00:19:58Z
dc.identifierIeee Transactions On Information Theory. Ieee-inst Electrical Electronics Engineers Inc, v. 59, n. 9, n. 5905, n. 5916, 2013.
dc.identifier0018-9448
dc.identifierWOS:000323455800045
dc.identifier10.1109/TIT.2013.2266398
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/58739
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/58739
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1286179
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionThe problem of searching for perfect codes has attracted great attention since the paper by Golomb and Welch, in which the existence of these codes over Lee metric spaces was considered. Since perfect codes are not very common, the problem of searching for quasi-perfect codes is also of great interest. In this aspect, also quasi-perfect Lee codes have been considered for 2-D and 3-D Lee metric spaces. In this paper, constructive methods for obtaining quasi-perfect codes over metric spaces modeled by means of Gaussian and Eisenstein-Jacobi integers are given. The obtained codes form ideals of the integer ring thus preserving the property of being geometrically uniform codes. Moreover, they are able to correct more error patterns than the perfect codes which may properly be used in asymmetric channels. Therefore, the results in this paper complement the constructions of perfect codes previously done for the same integer rings. Finally, decoding algorithms for the quasi-perfect codes obtained in this paper are provided and the relationship of the codes and the Lee metric ones is investigated.
dc.description59
dc.description9
dc.description5905
dc.description5916
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionSpanish Ministry of Science [TIN2010-21291-C02-02, AP2010-4900, CSD2007-00050]
dc.descriptionEuropean HiPEAC Network of Excellence
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFAPESP [2007/56052-8]
dc.descriptionCNPq [303059/2010-9]
dc.descriptionSpanish Ministry of Science [TIN2010-21291-C02-02, AP2010-4900, CSD2007-00050]
dc.languageen
dc.publisherIeee-inst Electrical Electronics Engineers Inc
dc.publisherPiscataway
dc.publisherEUA
dc.relationIeee Transactions On Information Theory
dc.relationIEEE Trans. Inf. Theory
dc.rightsfechado
dc.rightshttp://www.ieee.org/publications_standards/publications/rights/rights_policies.html
dc.sourceWeb of Science
dc.subjectCayley graphs
dc.subjectEisenstein-Jacobi (EJ) integer rings
dc.subjectGaussian integer rings
dc.subjectgeometrically uniform codes
dc.subjectquasi-perfect codes
dc.subjectLee Distance Codes
dc.subjectResource Placements
dc.subjectToroidal Networks
dc.subjectGaussian Integers
dc.subjectTori
dc.titleQuasi-Perfect Codes From Cayley Graphs Over Integer Rings
dc.typeArtículos de revistas


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