On D4t-Cocyclic Hadamard Matrices

In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t. Using this characterization, new classification results for certain cohomology classes of cocycles over D4t are obtained, extending existing...

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Detalles Bibliográficos
Autores: Álvarez Solano, Víctor, Armario Sampalo, José Andrés, 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:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/114849
Acceso en línea:https://hdl.handle.net/11441/114849
https://doi.org/10.1002/jcd.21510
Access Level:acceso abierto
Palabra clave:Hadamard matrix
Ito’s type Q Hadamard matrix
shift equivalence
Descripción
Sumario:In this paper, we describe some necessary and sufficient conditions for a set of coboundaries to yield a cocyclic Hadamard matrix over the dihedral group D4t. Using this characterization, new classification results for certain cohomology classes of cocycles over D4t are obtained, extending existing exhaustive calculations for cocyclic Hadamard matrices over D4t from order 36 to order 44. We also define some transformations over coboundaries, which preserve orthogonality of D4t -cocycles. These transformations are shown to correspond to Horadam’s bundle equivalence operations enriched with duals of cocycles.