On q-ary plateaued functions over Fq and their explicit characterizations

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dc.contributor.authorMesnager, Sihem
dc.contributor.authorOzbudak, Ferruh
dc.contributor.authorSinak, Ahmet
dc.contributor.authorCohen, Gerard
dc.date.accessioned2024-02-23T14:02:44Z
dc.date.available2024-02-23T14:02:44Z
dc.date.issued2019
dc.departmentNEÜen_US
dc.description.abstractPlateaued and bent functions play a significant role in cryptography, sequence theory, coding theory and combinatorics. In 1997, Coulter and Matthews redefined bent functions over any finite field F-q where q is a prime power, and established their properties. The objective of this work is to redefine the notion of plateaued functions over F-q, and to present several explicit characterizations of those functions. We first give, over F-q, the notion of q-ary plateaued functions, which relies on the concept of the Walsh-Hadamard transform in terms of canonical additive character of F-q. We then give a concrete example of q-ary plateaued function, that is not vectorial p-ary plateaued function. This suggests that the study of plateaued-ness is also significant for q-ary functions over Fq. We finally characterize q-ary plateaued functions in terms of derivatives, Walsh power moments and autocorrelation functions. (C) 2018 Elsevier Ltd. All rights reserved.en_US
dc.description.sponsorshipTUBITAK (the Scientific and Technological Research Council of Turkey) [BIDEB 2214/A]en_US
dc.description.sponsorshipThe third author is supported by TUBITAK (the Scientific and Technological Research Council of Turkey), program no: BIDEB 2214/Aen_US
dc.identifier.doi10.1016/j.ejc.2018.02.025
dc.identifier.endpage81en_US
dc.identifier.issn0195-6698
dc.identifier.issn1095-9971
dc.identifier.scopus2-s2.0-85042490121en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage71en_US
dc.identifier.urihttps://doi.org/10.1016/j.ejc.2018.02.025
dc.identifier.urihttps://hdl.handle.net/20.500.12452/11830
dc.identifier.volume80en_US
dc.identifier.wosWOS:000474675900009en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAcademic Press Ltd- Elsevier Science Ltden_US
dc.relation.ispartofEuropean Journal Of Combinatoricsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject[Keyword Not Available]en_US
dc.titleOn q-ary plateaued functions over Fq and their explicit characterizationsen_US
dc.typeArticleen_US

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