A new class of monomial bent functions

We study the Boolean functions , of the form f(x)=Tr(λxd) with d=22r+2r+1 and λ F2n. Our main result is the characterization of those λ for which fλ are bent. We show also that the set of these cubic bent functions contains a subset, which with the constantly zero function forms a vector space of dimension 2r over F2. Further we determine the Walsh spectra of some related quadratic functions, the derivatives of the functions fλ.