Boolean Functions meet Combinatorics

In this project, we suggest a completely novel approach to studiying vectorial functions pn vector spaces over finite fields. The novelty is the fact that we are going to describe the important differential properties of Boolean functions in terms of design theory. This may open a completely new approach to the investigation of differential properties of Boolean functions. We also expect that the well-known ninlinearity measure of functions via the Walsh transform can be extended by replacing the classical Sylvester-Hadamard matrix by a different Hadamard matrix.