Coset leaders of the first-order Reed-Muller codes in four new classes of Boolean functions

The notion of coset leader has applications in coding theory and cryptography. In this paper, we extend a recent study of the coset leaders of the first order Reed-Muller codes to four classes of Boolean functions which have played an important role in diverse domains of Boolean functions, and whose study was missing in this context. We characterize the coset leaders that belong to the classes of Niho functions, threshold functions (which include majority functions as an important particular case), a class of functions generalizing the Kasami-Tokura functions and a class of functions with 2k-valued Walsh spectra that we introduce and which is a generalization of the recently introduced classes of functions having respectively 4 and 6 values in their Walsh spectrum.