Generating binary partial Hadamard matrices

This paper deals with partial binary Hadamard matrices. Although there is a fast simple way to generate about a half (which is the best asymptotic bound known so far, see de Launey (2000) and de Launey and Gordon (2001)) of a full Hadamard matrix, it cannot provide larger partial Hadamard matrices b...

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Autores: Álvarez Solano, Víctor, Armario Sampalo, José Andrés, Falcón Ganfornina, Raúl Manuel, Frau García, María Dolores, Gudiel Rodríguez, Félix, Güemes Alzaga, María Belén, Osuna Lucena, Amparo
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/89658
Acceso en línea:https://hdl.handle.net/11441/89658
https://doi.org/10.1016/j.dam.2018.12.008
Access Level:acceso abierto
Palabra clave:Partial Hadamard matrix
Hadamard Graph
Clique
Constraint satisfaction problem
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spelling Generating binary partial Hadamard matricesÁlvarez Solano, VíctorArmario Sampalo, José AndrésFalcón Ganfornina, Raúl ManuelFrau García, María DoloresGudiel Rodríguez, FélixGüemes Alzaga, María BelénOsuna Lucena, AmparoPartial Hadamard matrixHadamard GraphCliqueConstraint satisfaction problemThis paper deals with partial binary Hadamard matrices. Although there is a fast simple way to generate about a half (which is the best asymptotic bound known so far, see de Launey (2000) and de Launey and Gordon (2001)) of a full Hadamard matrix, it cannot provide larger partial Hadamard matrices beyond this bound. In order to overcome such a limitation, we introduce a particular subgraph Gt of Ito’s Hadamard Graph Δ(4t) (Ito, 1985), and study some of its properties,which facilitates that a procedure may be designed for constructing large partial Hadamard matrices. The key idea is translating the problem of extending a given clique in Gt into a Constraint Satisfaction Problem, to be solved by Minion (Gent et al., 2006). Actually, iteration of this process ends with large partial Hadamard matrices, usually beyond the bound of half a full Hadamard matrix, at least as our computation capabilities have led us thus far.ElsevierMatemática Aplicada I2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/89658https://doi.org/10.1016/j.dam.2018.12.008reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete Applied Mathematics, 263 (june 2019), 2-7.https://www.sciencedirect.com/science/article/pii/S0166218X18306516info:eu-repo/semantics/openAccessoai:idus.us.es:11441/896582026-06-17T12:51:07Z
dc.title.none.fl_str_mv Generating binary partial Hadamard matrices
title Generating binary partial Hadamard matrices
spellingShingle Generating binary partial Hadamard matrices
Álvarez Solano, Víctor
Partial Hadamard matrix
Hadamard Graph
Clique
Constraint satisfaction problem
title_short Generating binary partial Hadamard matrices
title_full Generating binary partial Hadamard matrices
title_fullStr Generating binary partial Hadamard matrices
title_full_unstemmed Generating binary partial Hadamard matrices
title_sort Generating binary partial Hadamard matrices
dc.creator.none.fl_str_mv Álvarez Solano, Víctor
Armario Sampalo, José Andrés
Falcón Ganfornina, Raúl Manuel
Frau García, María Dolores
Gudiel Rodríguez, Félix
Güemes Alzaga, María Belén
Osuna Lucena, Amparo
author Álvarez Solano, Víctor
author_facet Álvarez Solano, Víctor
Armario Sampalo, José Andrés
Falcón Ganfornina, Raúl Manuel
Frau García, María Dolores
Gudiel Rodríguez, Félix
Güemes Alzaga, María Belén
Osuna Lucena, Amparo
author_role author
author2 Armario Sampalo, José Andrés
Falcón Ganfornina, Raúl Manuel
Frau García, María Dolores
Gudiel Rodríguez, Félix
Güemes Alzaga, María Belén
Osuna Lucena, Amparo
author2_role author
author
author
author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Partial Hadamard matrix
Hadamard Graph
Clique
Constraint satisfaction problem
topic Partial Hadamard matrix
Hadamard Graph
Clique
Constraint satisfaction problem
description This paper deals with partial binary Hadamard matrices. Although there is a fast simple way to generate about a half (which is the best asymptotic bound known so far, see de Launey (2000) and de Launey and Gordon (2001)) of a full Hadamard matrix, it cannot provide larger partial Hadamard matrices beyond this bound. In order to overcome such a limitation, we introduce a particular subgraph Gt of Ito’s Hadamard Graph Δ(4t) (Ito, 1985), and study some of its properties,which facilitates that a procedure may be designed for constructing large partial Hadamard matrices. The key idea is translating the problem of extending a given clique in Gt into a Constraint Satisfaction Problem, to be solved by Minion (Gent et al., 2006). Actually, iteration of this process ends with large partial Hadamard matrices, usually beyond the bound of half a full Hadamard matrix, at least as our computation capabilities have led us thus far.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/89658
https://doi.org/10.1016/j.dam.2018.12.008
url https://hdl.handle.net/11441/89658
https://doi.org/10.1016/j.dam.2018.12.008
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete Applied Mathematics, 263 (june 2019), 2-7.
https://www.sciencedirect.com/science/article/pii/S0166218X18306516
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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