Generalized Bent Criteria for Boolean Functions (I)

Generalizations of the bent property of a Boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic Boolean functions are related to simple graphs and it is shown that the orbit generated by successive local complementations on a graph can be found within the transform spectra under investigation. The flat spectra of a quadratic Boolean function are related to modified versions of its associated adjacency matrix.