Monomial bent functions

In this correspondence, we focus on bent functions of the form F(2 ⁿ) rarr F(2) where x rarr Tr(alphax^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