Bent functions, spreads, and o-polynomials

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dc.contributor.authorÇeşmelioğlu, Ayça
dc.contributor.authorMeidl, Wilfried
dc.contributor.authorPott, Alexander
dc.date.accessioned2021-05-15T12:40:36Z
dc.date.available2021-05-15T12:40:36Z
dc.date.issued2015
dc.departmentMühendislik ve Doğa Bilimleri Fakültesi, Temel Bilimler Bölümüen_US
dc.description.abstractWe show that bent functions f from F(p)m x F(p)m to F-p, which are constant or affine on the elements of a given spread of F(p)m x F(p)m, either arise from partial spread bent functions, or they are Boolean and a generalization of Dillon's class H. For spreads of a presemifield S, we show that a bent function of the second class corresponds to an o-polynomial of a presemifield in the Knuth orbit of S. In contrast to the finite fields case, we have to consider pairs of (pre) semifields in a Knuth orbit. We give a canonical example of an o-polynomial for commutative presemifields (which also defines a hyperoval on the semifield plane) and show that the corresponding bent functions belong to the completed Maiorana-McFarland class. Using Albert's twisted fields and Kantor's family of presemifields, we explicitly present examples of such bent functions.en_US
dc.description.sponsorshipTubitak BIDEB 2219 Scholarship ProgrammeTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)en_US
dc.description.sponsorshipThis author's research was supported by the Tubitak BIDEB 2219 Scholarship Programme.en_US
dc.identifier.doi10.1137/140963273
dc.identifier.endpage867en_US
dc.identifier.issn0895-4801
dc.identifier.issn1095-7146
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-84938075526
dc.identifier.scopusqualityQ2
dc.identifier.startpage854en_US
dc.identifier.urihttps://doi.org/10.1137/140963273
dc.identifier.urihttps://hdl.handle.net/20.500.12939/631
dc.identifier.volume29en_US
dc.identifier.wosWOS:000357409700010
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÇeşmelioğlu, Ayça
dc.language.isoen
dc.publisherSiam Publicationsen_US
dc.relation.ispartofSiam Journal on Discrete Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBent Functionen_US
dc.subjectProjective Planeen_US
dc.subjectSemifielden_US
dc.subjectHyperovalen_US
dc.titleBent functions, spreads, and o-polynomials
dc.typeArticle

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