Hadamard Z₂Z₄Q₈-codes

Hadamard Z₂Z₄Q₈-codes are Hadamard binary codes coming from a subgroup of the direct product of Z₂, Z₄ and Q ₈ groups, where Q ₈ is the quaternionic group. We characterize Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and we show that all these codes can be represe...

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Detalles Bibliográficos
Autores: Montolio, Pere, Rifà i Coma, Josep|||0000-0001-9199-4001
Tipo de recurso: capítulo de libro
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:142878
Acceso en línea:https://ddd.uab.cat/record/142878
https://dx.doi.org/urn:doi:10.1007/978-3-319-17296-5_29
Access Level:acceso abierto
Palabra clave:Dimension of the kernel
Error-correcting codes
Hadamard codes
Rank
Z₂Z₄-linear codes
Z₂Z₄Q₈-codes
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spelling Hadamard Z₂Z₄Q₈-codesrank and kernelMontolio, PereRifà i Coma, Josep|||0000-0001-9199-4001Dimension of the kernelError-correcting codesHadamard codesRankZ₂Z₄-linear codesZ₂Z₄Q₈-codesHadamard Z₂Z₄Q₈-codes are Hadamard binary codes coming from a subgroup of the direct product of Z₂, Z₄ and Q ₈ groups, where Q ₈ is the quaternionic group. We characterize Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and we show that all these codes can be represented in a standard form, from a set of generators. On the other hand, we show that there exist Hadamard Z₂Z₄Q₈-codes with any given pair of allowable parameters for the rank and dimension of the kernel.Springer 22015-01-0120152015-01-01Capítol de llibrehttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://ddd.uab.cat/record/142878https://dx.doi.org/urn:doi:10.1007/978-3-319-17296-5_29reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen 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:1428782026-06-06T12:50:31Z
dc.title.none.fl_str_mv Hadamard Z₂Z₄Q₈-codes
rank and kernel
title Hadamard Z₂Z₄Q₈-codes
spellingShingle Hadamard Z₂Z₄Q₈-codes
Montolio, Pere
Dimension of the kernel
Error-correcting codes
Hadamard codes
Rank
Z₂Z₄-linear codes
Z₂Z₄Q₈-codes
title_short Hadamard Z₂Z₄Q₈-codes
title_full Hadamard Z₂Z₄Q₈-codes
title_fullStr Hadamard Z₂Z₄Q₈-codes
title_full_unstemmed Hadamard Z₂Z₄Q₈-codes
title_sort Hadamard Z₂Z₄Q₈-codes
dc.creator.none.fl_str_mv Montolio, Pere
Rifà i Coma, Josep|||0000-0001-9199-4001
author Montolio, Pere
author_facet Montolio, Pere
Rifà i Coma, Josep|||0000-0001-9199-4001
author_role author
author2 Rifà i Coma, Josep|||0000-0001-9199-4001
author2_role author
dc.subject.none.fl_str_mv Dimension of the kernel
Error-correcting codes
Hadamard codes
Rank
Z₂Z₄-linear codes
Z₂Z₄Q₈-codes
topic Dimension of the kernel
Error-correcting codes
Hadamard codes
Rank
Z₂Z₄-linear codes
Z₂Z₄Q₈-codes
description Hadamard Z₂Z₄Q₈-codes are Hadamard binary codes coming from a subgroup of the direct product of Z₂, Z₄ and Q ₈ groups, where Q ₈ is the quaternionic group. We characterize Hadamard Z₂Z₄Q₈-codes as a quotient of a semidirect product of Z₂Z₄-linear codes and we show that all these codes can be represented in a standard form, from a set of generators. On the other hand, we show that there exist Hadamard Z₂Z₄Q₈-codes with any given pair of allowable parameters for the rank and dimension of the kernel.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
dc.type.none.fl_str_mv Capítol de llibre
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/142878
https://dx.doi.org/urn:doi:10.1007/978-3-319-17296-5_29
url https://ddd.uab.cat/record/142878
https://dx.doi.org/urn:doi:10.1007/978-3-319-17296-5_29
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
repository.name.fl_str_mv
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