Difference sets are of central interest in finite geometry and design theory. One of the main
techniques to investigate abelian difference sets is a discrete version of the classical Fourier …

We present a recursive construction for difference sets which unifies the Hadamard,
McFarland, and Spence parameter families and deals with all abelian groups known to …

During the past decade, perfect, almost perfect and maximum nonlinear functions on finite
fields have been thoroughly investigated. The main tool to investigate these functions is the …

Bent functions from a vector space V _n V n over F _2 F 2 of even dimension n= 2m n= 2 m
into the cyclic group Z _ 2^ k Z 2 k, or equivalently, relative difference sets in V _n * Z _ 2^ k …

Recently, many new almost perfect nonlinear (APN) and almost bent (AB) functions have
been constructed. These functions n 2→ n 2 play an important role in cryptography. In this …

We show that for an odd prime p the exponent of an abelian group of order pa+ b containing
a relative (pa, pb, pa, pa− b)-difference set cannot exceed p⌊ a/2⌋+ 1. Furthermore, we give …

We present results related to vectorial plateaued functions and map**s whose derivatives
are 2s-to-1 functions. The results in this note generalize facts about almost perfect nonlinear …

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It
is shown that a closed linked system of RDSs is always graded by a group. Based on this …

Cocyclic matrices have the form M= ψ (g, h) _ g, h ∈ G, where G is a finite group, C is a finite
abelian group and ψ: G× G→ C is a (two-dimensional) cocycle; that is, ψ (g, h) ψ (gh, k)= ψ …

Abelian relative difference sets of parameters (m, n, k, λ)=(pa, p, pa, pa− 1) are studied in
this paper. In particular, we show that for an abelian group G of order p 2c+ 1 and a …