Hyperbent functions are special Boolean functions which composited with any bijective power function have maximal distance from affine functions. This paper is devoted to a class of hyperbent functions having the form \(f_{a,b}^{d}(x)={{\,\textrm{Tr}\,}}_{1}^{2n}(a(x^{2^n-1}+b)^{d})\) for \(a, \, b\in \mathbb {F}_{2^{2n}}^*\) . For \(a\in \mathbb {F}_{2^{n}}^*\) and several exponents d, we characterize parameters a and b, which yield hyperbent functions \(f_{a,b}^{d}(x)\) , via partial exponential sums of Dickson polynomials; in a particular case when \(b=1\) we uncover that hyperbent functions can be derived from bijective power functions, including almost nonlinear power functions for odd n. When \(a\in \mathbb {F}_{2^{2n}}\setminus \mathbb {F}_{2^n}\) and \(b=1\) , we introduce a parameterized method to reduce the computation of involved exponential sums which also lead to explicit hyperbent functions.
