Vectorial bent functions and partial difference sets
Küçük Resim Yok
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Bent Function, Vectorial Bent Function, Partial Difference Set, Cyclotomy, Maiorana Mcfarland Function
Kaynak
Designs Codes and Cryptography
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
89
Sayı
10
