A NOVEL ALGORITHM ENUMERATING BENT FUNCTIONS

By the relationship between the Walsh spectra at partial points and the Walsh spectra of its sub-functions, by the action of general linear group on the set of Boolean functions, and by the Reed-Muller transform, a novel method is developed, which can theoretically construct all bent functions. With this method, we enumerate all bent functions in 6 variables; in 8-variable case, our method is more efficient than the method presented by Clark though we still can not enumerate all bent functions; enumeration of all homogeneous bent functions of degree 3 in eight variables can be done in one minute by a P4 1.7G HZ computer; construction of homogenous bent function of degree 3 in 10 variables is efficient too; the nonexistence of homogeneous bent functions in 10 variables of degree 4 is prove