Monomial bent functions
In this correspondence, we focus on bent functions of the form F-2(n) -> F-2 where x -> T-r(ax(d)). The main contribution of this correspondence is, that we prove that for n = 4r, r odd, the exponent d = (2(r) + 1)(2) allows the construction of bent functions. This open question has been posed by Canteaut based on computer experiments. As a consequence for each of the well understood families of bent functions, we now know an exponent d that yields to bent functions of the given type.
bent functions boolean functions monomial boolean functions power functions trace expansion