Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices

In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering Butson matrices that are cocyclic rather than strictly group i...

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Detalles Bibliográficos
Autores: Armario Sampalo, José Andrés, Egan, Ronan, Flannery, D. L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/149665
Acceso en línea:https://hdl.handle.net/11441/149665
https://doi.org/10.1007/s12095-023-00657-z
Access Level:acceso abierto
Palabra clave:Generalized bent functions
Butson Hadamard matrices
Generalized perfect arrays
Cocycles
Descripción
Sumario:In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We establish a broader network of equivalences by considering Butson matrices that are cocyclic rather than strictly group invariant. This result has several applications; for example, to the construction of Boolean functions whose expansions are generalized partially bent functions, including cases where no bent function can exist.