Bent Functions of Maximal Degree

In this paper, a technique for constructing p-ary bent functions from plateaued functions is presented. This generalizes earlier techniques of constructing bent from near-bent functions. The Fourier spectrum of quadratic monomials is analyzed, and examples of quadratic functions with highest possible absolute values in their Fourier spectrum are given. Applying the construction of bent functions to the latter class of functions yields bent functions attaining upper bounds for the algebraic degree when p= 3,5. Until now, no construction of bent functions attaining these bounds was known.