Hyperbent functions, Kloosterman sums and Dickson polynomials

This paper is devoted to the classification of hyperbent functions, i.e., bent functions which are bent up to a primitive root change. We first exhibit an infinite class of monomial functions which are not hyperbent. It implies notably that Kloosterman sums at point 1 on F_2m cannot be zero, unless m = 4. Further, we show that hyperbent functions with multiple trace terms can be described by means of Dickson polynomials.