Generalized Semi-bent and Partially Bent Boolean Functions
Brajesh Kumar Singh · Mathematical Sciences Letters · 2013
In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis.We investigate a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function.It is demonstrated that σ f = 2 2n+s for every s-plateaued generalized Boolean function in n variables.Two classes of generalized semi-bent Boolean functions are constructed.We have constructed a class of generalized semi-bent functions in (n + 1) variables from generalized semi-bent functions in n variables and identify a subclass of it for which σ f and f both have optimal value.Finally, some construction on generalized partially bent Boolean functions are given.