The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z

Bibliographic Details
Main Author: Cruz, Catarina Maria Neto da
Publication Date: 2016
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/16660
Summary: The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n ³ 3 and r ³ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture has resisted, although its validity has been proved for some particular values of n and r, namely: 3 £ n £ 5 and r ³ 2; n = 6 and r = 2. Here we give a contribution for the proof of the Golomb-Welch conjecture which reinforces it, proving the non-existence of perfect 2-error correcting Lee codes of word length 7 over Z.
id RCAP_34e801eff70ff27b5bf3f60a31e7cc65
oai_identifier_str oai:ria.ua.pt:10773/16660
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
spelling The non-existence of perfect 2-error correcting Lee codes of word length 7 over ZMatemáticaCódigos de correcção de errosConjectura de Golomb-WelchThe Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n ³ 3 and r ³ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture has resisted, although its validity has been proved for some particular values of n and r, namely: 3 £ n £ 5 and r ³ 2; n = 6 and r = 2. Here we give a contribution for the proof of the Golomb-Welch conjecture which reinforces it, proving the non-existence of perfect 2-error correcting Lee codes of word length 7 over Z.A conjetura de Golomb-Welch estabelece que não existem códigos de Lee perfeitos, corretores de r-erros, de palavras de comprimento n sobre Z para n ³ 3 e r ³ 2. Este problema tem recebido particular atenção devido à sua importância em aplicações em várias áreas que não apenas a da matemática e das ciências da computação. Apesar de terem sido obtidos muitos resultados no sentido de provar a conjetura, esta tem resistido estando estabelecida apenas para alguns valores particulares de n e r, nomeadamente: 3 £ n £ 5 e r ³ 2; n = 6 e r = 2. Nesta tese é dada uma contribuição que reforça a conjetura, sendo provada a não existência de códigos de Lee perfeitos, corretores de 2-erros, de palavras de comprimento 7 sobre Z.Universidade de Aveiro2018-07-20T14:00:58Z2016-05-10T00:00:00Z2016-05-102017-05-10T14:00:00Zdoctoral thesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10773/16660TID:101418280engCruz, Catarina Maria Neto dainfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:59:17Zoai:ria.ua.pt:10773/16660Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:53:34.421334Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
title The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
spellingShingle The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
Cruz, Catarina Maria Neto da
Matemática
Códigos de correcção de erros
Conjectura de Golomb-Welch
title_short The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
title_full The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
title_fullStr The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
title_full_unstemmed The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
title_sort The non-existence of perfect 2-error correcting Lee codes of word length 7 over Z
author Cruz, Catarina Maria Neto da
author_facet Cruz, Catarina Maria Neto da
author_role author
dc.contributor.author.fl_str_mv Cruz, Catarina Maria Neto da
dc.subject.por.fl_str_mv Matemática
Códigos de correcção de erros
Conjectura de Golomb-Welch
topic Matemática
Códigos de correcção de erros
Conjectura de Golomb-Welch
description The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n ³ 3 and r ³ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture has resisted, although its validity has been proved for some particular values of n and r, namely: 3 £ n £ 5 and r ³ 2; n = 6 and r = 2. Here we give a contribution for the proof of the Golomb-Welch conjecture which reinforces it, proving the non-existence of perfect 2-error correcting Lee codes of word length 7 over Z.
publishDate 2016
dc.date.none.fl_str_mv 2016-05-10T00:00:00Z
2016-05-10
2017-05-10T14:00:00Z
2018-07-20T14:00:58Z
dc.type.driver.fl_str_mv doctoral thesis
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/16660
TID:101418280
url http://hdl.handle.net/10773/16660
identifier_str_mv TID:101418280
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade de Aveiro
publisher.none.fl_str_mv Universidade de Aveiro
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833594168972148736

Similar Items