New results on nonexistence of generalized bent functions

We get two kinds of new results on nonexistence of generalized bent function. The first one is Based on Feng\u27s results by using Schmidt\u27s field descent method. For the second kind, considering special property of the field $\mathbb{Q}(\zeta_{23^e})$, We get new nonexistence results of generalized bent functions with type $[3,2\cdot23^e]$

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