Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)

Detalhes bibliográficos
Autor(a) principal: Cruz, Catarina N.
Data de Publicação: 2018
Outros Autores: Breda, Ana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/22991
Resumo: The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over ℤ for n ≥ 3 and r ≥ 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 is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.
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spelling Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)Perfect Lee codesGolomb-Welch conjectureSpace tilingsThe Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over ℤ for n ≥ 3 and r ≥ 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 is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.De Gruyter2018-04-27T14:58:34Z2018-04-02T00:00:00Z2018-04-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/22991eng2391-545510.1515/math-2018-0027Cruz, Catarina N.Breda, Anainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:44:51Zoai:ria.ua.pt:10773/22991Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:56:55.596947Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
title Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
spellingShingle Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
Cruz, Catarina N.
Perfect Lee codes
Golomb-Welch conjecture
Space tilings
title_short Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
title_full Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
title_fullStr Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
title_full_unstemmed Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
title_sort Restriction conditions on PL(7, 2) codes (3 ≤ |_i| ≤ 7)
author Cruz, Catarina N.
author_facet Cruz, Catarina N.
Breda, Ana
author_role author
author2 Breda, Ana
author2_role author
dc.contributor.author.fl_str_mv Cruz, Catarina N.
Breda, Ana
dc.subject.por.fl_str_mv Perfect Lee codes
Golomb-Welch conjecture
Space tilings
topic Perfect Lee codes
Golomb-Welch conjecture
Space tilings
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 and r ≥ 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 is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.
publishDate 2018
dc.date.none.fl_str_mv 2018-04-27T14:58:34Z
2018-04-02T00:00:00Z
2018-04-02
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/22991
url http://hdl.handle.net/10773/22991
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2391-5455
10.1515/math-2018-0027
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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