Vectorial bent functions and partial difference sets
| dc.authorid | Pirsic, Isabel/0000-0003-3386-3075 | |
| dc.contributor.author | Cesmelioglu, Ayca | |
| dc.contributor.author | Meidl, Wilfried | |
| dc.contributor.author | Pirsic, Isabel | |
| dc.date.accessioned | 2024-07-18T20:40:39Z | |
| dc.date.available | 2024-07-18T20:40:39Z | |
| dc.date.issued | 2021 | |
| dc.department | İstanbul Bilgi Üniversitesi | en_US |
| dc.description.abstract | The 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.sponsorship | FWF [P 30966]; FWF Project, Special Research Program Quasi-Monte Carlo Methods: Theory and Applications [F5508-N26] | en_US |
| dc.description.sponsorship | W.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.doi | 10.1007/s10623-021-00919-y | |
| dc.identifier.endpage | 2330 | en_US |
| dc.identifier.issn | 0925-1022 | |
| dc.identifier.issn | 1573-7586 | |
| dc.identifier.issue | 10 | en_US |
| dc.identifier.scopus | 2-s2.0-85112435598 | en_US |
| dc.identifier.scopusquality | Q1 | en_US |
| dc.identifier.startpage | 2313 | en_US |
| dc.identifier.uri | https://doi.org/10.1007/s10623-021-00919-y | |
| dc.identifier.uri | https://hdl.handle.net/11411/7166 | |
| dc.identifier.volume | 89 | en_US |
| dc.identifier.wos | WOS:000684916200001 | en_US |
| dc.identifier.wosquality | Q2 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Springer | en_US |
| dc.relation.ispartof | Designs Codes and Cryptography | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Bent Function | en_US |
| dc.subject | Vectorial Bent Function | en_US |
| dc.subject | Partial Difference Set | en_US |
| dc.subject | Cyclotomy | en_US |
| dc.subject | Maiorana Mcfarland Function | en_US |
| dc.title | Vectorial bent functions and partial difference sets | en_US |
| dc.type | Article | en_US |
