Cesmelioglu, AycaMeidl, WilfriedPirsic, Isabel2024-07-182024-07-1820210925-10221573-7586https://doi.org/10.1007/s10623-021-00919-yhttps://hdl.handle.net/11411/7166The 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.eninfo:eu-repo/semantics/closedAccessBent FunctionVectorial Bent FunctionPartial Difference SetCyclotomyMaiorana Mcfarland FunctionArticle2-s2.0-8511243559810.1007/s10623-021-00919-y233010Q1231389Q2WOS:000684916200001