On the constructions of ZpZp2-linear generalized Hadamard codes

The ZZ-additive codes are subgroups of Z ×Z , and can be seen as linear codes over Z when α=0, Z-additive codes when α=0, or ZZ-additive codes when p=2. A ZZ-linear generalized Hadamard (GH) code is a GH code over Z which is the Gray map image of a ZZ-additive code. In this paper, we generalize some...

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Autores: Bhunia, Dipak Kumar|||0000-0003-4852-8739, Fernández Córdoba, Cristina|||0000-0001-5880-144X, Villanueva, M|||0000-0001-6179-0833
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:268175
Acceso en línea:https://ddd.uab.cat/record/268175
https://dx.doi.org/urn:doi:10.1016/j.ffa.2022.102093
Access Level:acceso abierto
Palabra clave:Generalized Hadamard code
Gray map
ZpZp2
-Linear code
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spelling On the constructions of ZpZp2-linear generalized Hadamard codesBhunia, Dipak Kumar|||0000-0003-4852-8739Fernández Córdoba, Cristina|||0000-0001-5880-144XVillanueva, M|||0000-0001-6179-0833Generalized Hadamard codeGray mapZpZp2-Linear codeThe ZZ-additive codes are subgroups of Z ×Z , and can be seen as linear codes over Z when α=0, Z-additive codes when α=0, or ZZ-additive codes when p=2. A ZZ-linear generalized Hadamard (GH) code is a GH code over Z which is the Gray map image of a ZZ-additive code. In this paper, we generalize some known results for ZZ-linear GH codes with p=2 to any p≥3 prime when α≠0. First, we give a recursive construction of ZZ-additive GH codes of type (α,α;t,t) with t,t≥1. We also present many different recursive constructions of ZZ-additive GH codes having the same type, and show that we obtain permutation equivalent codes after applying the Gray map. Finally, according to some computational results, we see that, unlike Z-linear GH codes, when p≥3 prime, the Z-linear GH codes are not included in the family of ZZ-linear GH codes with α≠0. Indeed, we observe that the constructed codes are not equivalent to the Z-linear GH codes for any s≥2. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/268175https://dx.doi.org/urn:doi:10.1016/j.ffa.2022.102093reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104664GB-I00Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2020/FI-SDUR-00475open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2681752026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the constructions of ZpZp2-linear generalized Hadamard codes
title On the constructions of ZpZp2-linear generalized Hadamard codes
spellingShingle On the constructions of ZpZp2-linear generalized Hadamard codes
Bhunia, Dipak Kumar|||0000-0003-4852-8739
Generalized Hadamard code
Gray map
ZpZp2
-Linear code
title_short On the constructions of ZpZp2-linear generalized Hadamard codes
title_full On the constructions of ZpZp2-linear generalized Hadamard codes
title_fullStr On the constructions of ZpZp2-linear generalized Hadamard codes
title_full_unstemmed On the constructions of ZpZp2-linear generalized Hadamard codes
title_sort On the constructions of ZpZp2-linear generalized Hadamard codes
dc.creator.none.fl_str_mv Bhunia, Dipak Kumar|||0000-0003-4852-8739
Fernández Córdoba, Cristina|||0000-0001-5880-144X
Villanueva, M|||0000-0001-6179-0833
author Bhunia, Dipak Kumar|||0000-0003-4852-8739
author_facet Bhunia, Dipak Kumar|||0000-0003-4852-8739
Fernández Córdoba, Cristina|||0000-0001-5880-144X
Villanueva, M|||0000-0001-6179-0833
author_role author
author2 Fernández Córdoba, Cristina|||0000-0001-5880-144X
Villanueva, M|||0000-0001-6179-0833
author2_role author
author
dc.subject.none.fl_str_mv Generalized Hadamard code
Gray map
ZpZp2
-Linear code
topic Generalized Hadamard code
Gray map
ZpZp2
-Linear code
description The ZZ-additive codes are subgroups of Z ×Z , and can be seen as linear codes over Z when α=0, Z-additive codes when α=0, or ZZ-additive codes when p=2. A ZZ-linear generalized Hadamard (GH) code is a GH code over Z which is the Gray map image of a ZZ-additive code. In this paper, we generalize some known results for ZZ-linear GH codes with p=2 to any p≥3 prime when α≠0. First, we give a recursive construction of ZZ-additive GH codes of type (α,α;t,t) with t,t≥1. We also present many different recursive constructions of ZZ-additive GH codes having the same type, and show that we obtain permutation equivalent codes after applying the Gray map. Finally, according to some computational results, we see that, unlike Z-linear GH codes, when p≥3 prime, the Z-linear GH codes are not included in the family of ZZ-linear GH codes with α≠0. Indeed, we observe that the constructed codes are not equivalent to the Z-linear GH codes for any s≥2.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/268175
https://dx.doi.org/urn:doi:10.1016/j.ffa.2022.102093
url https://ddd.uab.cat/record/268175
https://dx.doi.org/urn:doi:10.1016/j.ffa.2022.102093
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 PID2019-104664GB-I00
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2020/FI-SDUR-00475
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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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