Vectorial bent functions and partial difference sets

dc.authoridPirsic, Isabel/0000-0003-3386-3075
dc.contributor.authorCesmelioglu, Ayca
dc.contributor.authorMeidl, Wilfried
dc.contributor.authorPirsic, Isabel
dc.date.accessioned2024-07-18T20:40:39Z
dc.date.available2024-07-18T20:40:39Z
dc.date.issued2021
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractThe objective of this article is to broaden the understanding of the connections between bent functions and partial difference sets. Recently, the first two authors showed that the elements which a vectorial dual-bent function with certain additional properties maps to 0, form a partial difference set, which generalizes the connection between Boolean bent functions and Hadamard difference sets, and some later established connections between p-ary bent functions and partial difference sets to vectorial bent functions. We discuss the effects of coordinate transformations. As all currently known vectorial dual-bent functions F : F-p(n) -> F-p(s) are linear equivalent to l-forms, i.e., to functions satisfying F(beta x) = beta(l) F(x) for all beta is an element of F-p(s), we investigate properties of partial difference sets obtained from l-forms. We show that they are unions of cosets of F* p(s), which also can be seen as certain cyclotomic classes. We draw connections to known results on partial difference sets from cyclotomy. Motivated by experimental results, for a class of vectorial dual-bent functions from Fp(n) to Fp(s), we show that the preimage set of the squares of Fps forms a partial difference set. This extends earlier results on p-ary bent functions.en_US
dc.description.sponsorshipFWF [P 30966]; FWF Project, Special Research Program Quasi-Monte Carlo Methods: Theory and Applications [F5508-N26]en_US
dc.description.sponsorshipW.M. is supported by the FWF Project P 30966; I.P. is supported by the FWF Project F5508-N26, which is a part of the Special Research Program Quasi-Monte Carlo Methods: Theory and Applications. We like to thank the Associate Editor, and the reviewers for their comments.en_US
dc.identifier.doi10.1007/s10623-021-00919-y
dc.identifier.endpage2330en_US
dc.identifier.issn0925-1022
dc.identifier.issn1573-7586
dc.identifier.issue10en_US
dc.identifier.scopus2-s2.0-85112435598en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage2313en_US
dc.identifier.urihttps://doi.org/10.1007/s10623-021-00919-y
dc.identifier.urihttps://hdl.handle.net/11411/7166
dc.identifier.volume89en_US
dc.identifier.wosWOS:000684916200001en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofDesigns Codes and Cryptographyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBent Functionen_US
dc.subjectVectorial Bent Functionen_US
dc.subjectPartial Difference Seten_US
dc.subjectCyclotomyen_US
dc.subjectMaiorana Mcfarland Functionen_US
dc.titleVectorial bent functions and partial difference setsen_US
dc.typeArticleen_US

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