Bent and vectorial bent functions, partial difference sets, and strongly regular graphs

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dc.contributor.authorÇesmelioğlu, Ayça
dc.contributor.authorMeidl, Wilfried
dc.date.accessioned2021-05-15T12:41:33Z
dc.date.available2021-05-15T12:41:33Z
dc.date.issued2018
dc.departmentMühendislik ve Doğa Bilimleri Fakültesien_US
dc.descriptionCesmelioglu, Ayca/0000-0001-5049-9135
dc.description.abstractBent and vectorial bent functions have applications in cryptography and coding and are closely related to objects in combinatorics and finite geometry, like difference sets, relative difference sets, designs and divisible designs. Bent functions with certain additional properties yield partial difference sets of which the Cayley graphs are always strongly regular. In this article we continue research on connections between bent functions and partial difference sets respectively strongly regular graphs. For the first time we investigate relations between vectorial bent functions and partial difference sets. Remarkably, properties of the set of the duals of the components play here an important role. Seeing conventional bent functions as 1-dimensional vectorial bent functions, some earlier results on strongly regular graphs from bent functions follow from our more general results. Finally we describe a recursive construction of infinitely many partial difference sets with a secondary construction of p-ary bent functions.en_US
dc.description.sponsorshipAustrian Science Fund (FWF)Austrian Science Fund (FWF) [M 1767-N26]en_US
dc.description.sponsorshipThe second author is supported by the Austrian Science Fund (FWF) Project no. M 1767-N26.en_US
dc.identifier.doi10.3934/amc.2018041
dc.identifier.endpage705en_US
dc.identifier.issn1930-5346
dc.identifier.issn1930-5338
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85063159232
dc.identifier.scopusqualityQ1
dc.identifier.startpage691en_US
dc.identifier.urihttps://doi.org/10.3934/amc.2018041
dc.identifier.urihttps://hdl.handle.net/20.500.12939/820
dc.identifier.volume12en_US
dc.identifier.wosWOS:000444988000005
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÇesmelioğlu, Ayça
dc.language.isoen
dc.publisherAmer Inst Mathematical Sciences-Aimsen_US
dc.relation.ispartofAdvances in Mathematics of Communications
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBent Functionen_US
dc.subjectVectorial Boolean Functionen_US
dc.subjectPartial Difference Seten_US
dc.subjectStrongly Regular Graphen_US
dc.subjectDual Bent Functionen_US
dc.subjectWalsh Transformen_US
dc.titleBent and vectorial bent functions, partial difference sets, and strongly regular graphs
dc.typeArticle

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