Graphs of vectorial plateaued functions as difference sets

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dc.authorwosidOlmez, Oktay/AAI-1853-2020
dc.authorwosidCesmelioglu, Ayca/AAE-4933-2020
dc.contributor.authorCesmelioglu, Ayca
dc.contributor.authorOlmez, Oktay
dc.date.accessioned2024-07-18T20:42:38Z
dc.date.available2024-07-18T20:42:38Z
dc.date.issued2021
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractA function F : F-pn -> F-pm , is a vectorial s-plateaued function if for each component function F-b(mu) = Tr-n(bF(x)), b is an element of F-pm* and mu is an element of F-pn , the Walsh transform value vertical bar(F-b) over cap(mu)vertical bar is either 0 or p(n+s/2) . In this paper, we explore the relation between (vectorial) s-plateaued functions and partial geometric difference sets. Moreover, we establish the link between three-valued cross-correlation of p-ary sequences and vectorial s-plateaued functions. Using this link, we provide a partition of F-3n into partial geometric difference sets. Conversely, using a partition of F-3n into partial geometric difference sets, we construct ternary plateaued functions f : F-3n -> F-3. We also give a characterization of p-ary plateaued functions in terms of special matrices which enables us to give the link between such functions and second-order derivatives using a different approach. (C) 2020 Elsevier Inc. All rights reserved.en_US
dc.description.sponsorshipTUBITAK Research Grant [115F064]en_US
dc.description.sponsorshipOktay Olmez's research was supported by TUBITAK Research Grant Proj. No. 115F064.en_US
dc.identifier.doi10.1016/j.ffa.2020.101795
dc.identifier.issn1071-5797
dc.identifier.issn1090-2465
dc.identifier.scopus2-s2.0-85098195082en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1016/j.ffa.2020.101795
dc.identifier.urihttps://hdl.handle.net/11411/7367
dc.identifier.volume71en_US
dc.identifier.wosWOS:000620294000005en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherAcademic Press Inc Elsevier Scienceen_US
dc.relation.ispartofFinite Fields and Their Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectPartial Geometric Designsen_US
dc.subjectPartial Geometric Difference Setsen_US
dc.subjectPlateaued Functionsen_US
dc.subjectThree-Valued Cross-Correlation Functionen_US
dc.subjectBenten_US
dc.subjectCodesen_US
dc.titleGraphs of vectorial plateaued functions as difference setsen_US
dc.typeArticleen_US

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