On hadamard full propelinear codes with associated group C2t × C2

We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard...

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Autores: Bailera, Ivan|||0000-0001-6772-4802, Borges, Joaquim|||0000-0002-5774-4874, Rifà i Coma, Josep|||0000-0001-9199-4001
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:307004
Acceso en línea:https://ddd.uab.cat/record/307004
https://dx.doi.org/urn:doi:10.3934/amc.2020041
Access Level:acceso abierto
Palabra clave:Hadamard full propelinear codes
Hadamard matrices
Kernel
Rank
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spelling On hadamard full propelinear codes with associated group C2t × C2Bailera, Ivan|||0000-0001-6772-4802Borges, Joaquim|||0000-0002-5774-4874Rifà i Coma, Josep|||0000-0001-9199-4001Hadamard full propelinear codesHadamard matricesKernelRankWe introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/307004https://dx.doi.org/urn:doi:10.3934/amc.2020041reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 TIN2016-77918-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:3070042026-06-06T12:50:31Z
dc.title.none.fl_str_mv On hadamard full propelinear codes with associated group C2t × C2
title On hadamard full propelinear codes with associated group C2t × C2
spellingShingle On hadamard full propelinear codes with associated group C2t × C2
Bailera, Ivan|||0000-0001-6772-4802
Hadamard full propelinear codes
Hadamard matrices
Kernel
Rank
title_short On hadamard full propelinear codes with associated group C2t × C2
title_full On hadamard full propelinear codes with associated group C2t × C2
title_fullStr On hadamard full propelinear codes with associated group C2t × C2
title_full_unstemmed On hadamard full propelinear codes with associated group C2t × C2
title_sort On hadamard full propelinear codes with associated group C2t × C2
dc.creator.none.fl_str_mv Bailera, Ivan|||0000-0001-6772-4802
Borges, Joaquim|||0000-0002-5774-4874
Rifà i Coma, Josep|||0000-0001-9199-4001
author Bailera, Ivan|||0000-0001-6772-4802
author_facet Bailera, Ivan|||0000-0001-6772-4802
Borges, Joaquim|||0000-0002-5774-4874
Rifà i Coma, Josep|||0000-0001-9199-4001
author_role author
author2 Borges, Joaquim|||0000-0002-5774-4874
Rifà i Coma, Josep|||0000-0001-9199-4001
author2_role author
author
dc.subject.none.fl_str_mv Hadamard full propelinear codes
Hadamard matrices
Kernel
Rank
topic Hadamard full propelinear codes
Hadamard matrices
Kernel
Rank
description We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/307004
https://dx.doi.org/urn:doi:10.3934/amc.2020041
url https://ddd.uab.cat/record/307004
https://dx.doi.org/urn:doi:10.3934/amc.2020041
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 TIN2016-77918-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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