A construction of bent functions from plateaued functions

In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first known infinite classes of non-weakly regular bent functions. Weakly regular bent functions with certain additional properties can be used to construct partial difference sets and strongly regular graphs. We show how to obtain appropriate bent functions using our construction.