The characterizations of binary vector-output plateaued functions

The plateaued functions were first introduced by Zheng and Zhang and denote the Boolean functions on Vn such that their Walsh spectra are 0 or ±2^{n−r over 2}, where r is a even number with 0 ≤ r ≤ n. In this paper, we extend the plateaued functions to vector-output Boolean functions. We establish a sequence of important inequalities on the auto-correlation functions and the Walsh spectra of all nonzero linear combinations of the component functions. In particular, we characterize the vector-output plateaued functions by means of a sequence of equalities.