Secondary Constructions on Generalized Bent Functions
In this paper, the authors construct generalized bent Boolean functions in n + 2 variables from 4 generalized Boolean functions in n variables. They also show that the direct sum of two generalized bent Boolean functions is generalized bent. Finally, they identify a set of affine functions in which every function is generalized bent. In the recent years several authors have proposed generalizations of Boolean functions and studied the effect of Walsh-Hadamard transform on these classes. As in the Boolean case, in the generalized setup the functions which have at spectra with respect to the Walsh-Hadamard transform are said to be generalized bent and are of special interest. The classical notion of bent was invented by Rothaus.