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

Bibliographic Details
Main Author: Cruz, Catarina N.
Publication Date: 2018
Other Authors: Breda, Ana
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/22991
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 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:14:12Zoai:ria.ua.pt:10773/22991Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:01:38.290519Repositórios 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 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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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
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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
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