dc.creator | Álvarez Solano, Víctor | es |
dc.creator | Armario Sampalo, José Andrés | es |
dc.creator | Falcón Ganfornina, Raúl Manuel | es |
dc.creator | Frau García, María Dolores | es |
dc.creator | Gudiel Rodríguez, Félix | es |
dc.creator | Güemes Alzaga, María Belén | es |
dc.creator | Osuna Lucena, Amparo | es |
dc.date.accessioned | 2020-06-13T07:50:00Z | |
dc.date.available | 2020-06-13T07:50:00Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Álvarez Solano, V., Armario Sampalo, J.A., Falcón Ganfornina, R.M., Frau García, M.D., Gudiel Rodríguez, F., Güemes Alzaga, M.B. y Osuna Lucena, A. (2020). On Cocyclic Hadamard Matrices over Goethals-Seidel Loops. Mathematics, 8 (1) | |
dc.identifier.issn | 2227-7390 | es |
dc.identifier.uri | https://hdl.handle.net/11441/97765 | |
dc.description.abstract | About twenty-five years ago, Horadam and de Launey introduced the cocyclic development
of designs, from which the notion of cocyclic Hadamard matrices developed over a group was readily
derived. Much more recently, it has been proved that this notion may naturally be extended to
define cocyclic Hadamard matrices developed over a loop. This paper delves into this last topic by
introducing the concepts of coboundary, pseudocoboundary and pseudococycle over a quasigroup,
and also the notion of the pseudococyclic Hadamard matrix. Furthermore, Goethals-Seidel loops
are introduced as a family of Moufang loops so that every Hadamard matrix of Goethals-Seidel type
(which is known not to be cocyclically developed over any group) is actually pseudococyclically
developed over them. Finally, we also prove that, no matter if they are pseudococyclic matrices,
the usual cocyclic Hadamard test is unexpectedly applicable. | es |
dc.description.sponsorship | Junta de Andalucía FQM-016 | es |
dc.format | application/pdf | es |
dc.format.extent | 23 | es |
dc.language.iso | eng | es |
dc.publisher | MDPI | es |
dc.relation.ispartof | Mathematics, 8 (1) | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Hadamard matrix | es |
dc.subject | Cocyclic matrix | es |
dc.subject | Quasigroup | es |
dc.subject | Goethals-Seidel array | es |
dc.title | On Cocyclic Hadamard Matrices over Goethals-Seidel Loops | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) | es |
dc.relation.projectID | FQM-016 | es |
dc.relation.publisherversion | https://www.mdpi.com/2227-7390/8/1/24 | es |
dc.identifier.doi | 10.3390/math8010024 | es |
dc.journaltitle | Mathematics | es |
dc.publication.volumen | 8 | es |
dc.publication.issue | 1 | es |
dc.contributor.funder | Junta de Andalucía | es |