There are infinitely many bent functions for which the dual is not bent

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dc.contributor.authorCeşmelioğlu, Ayça
dc.contributor.authorMeidl, Wilfried
dc.contributor.authorPott, Alexander
dc.date.accessioned2021-05-15T12:37:02Z
dc.date.available2021-05-15T12:37:02Z
dc.date.issued2016
dc.departmentMühendislik ve Doğa Bilimleri Fakültesi, Temel Bilimler Bölümüen_US
dc.descriptionCesmelioglu, Ayca/0000-0001-5049-9135
dc.description.abstractBent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs, since their duals are also bent functions. In general, this does not apply to non-weakly regular bent functions. However, the first known construction of non-weakly regular bent functions by Cesmelioglu et al. yields bent functions for which the dual is also bent. In this paper, the first construction of non-weakly regular bent functions for which the dual is not bent is presented. We call such functions nondual-bent functions. Until now, only sporadic examples found via computer search were known. We then show that with the direct sum of bent functions and with the construction by Cesmelioglu et al., one can obtain infinitely many non-dual-bent functions once one example of a non-dual-bent function is known.en_US
dc.description.sponsorshipAustrian Science FundAustrian Science Fund (FWF) [M 1767-N26]; Austrian Science Fund (FWF)Austrian Science Fund (FWF) [M 1767] Funding Source: researchfishen_US
dc.description.sponsorshipW. Meidl was supported by the Austrian Science Fund under Project M 1767-N26.en_US
dc.identifier.doi10.1109/TIT.2016.2586081
dc.identifier.endpage5208en_US
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.issue9en_US
dc.identifier.scopus2-s2.0-84983565519
dc.identifier.scopusqualityQ1
dc.identifier.startpage5204en_US
dc.identifier.urihttps://doi.org/10.1109/TIT.2016.2586081
dc.identifier.urihttps://hdl.handle.net/20.500.12939/463
dc.identifier.volume62en_US
dc.identifier.wosWOS:000382442300028
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorCeşmelioğlu, Ayça
dc.language.isoen
dc.publisherIeee-Inst Electrical Electronics Engineers Incen_US
dc.relation.ispartofIeee Transactions on Information Theory
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBent Functionen_US
dc.subjectDualen_US
dc.subjectWalsh Transformen_US
dc.subjectVectorial Functionen_US
dc.subjectNon-Weakly Regularen_US
dc.titleThere are infinitely many bent functions for which the dual is not bent
dc.typeArticle

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