Coset leaders of the first order Reed-Muller codes in the classes of Niho and Threshold functions

The notion of coset leader has applications in coding theory and cryptography. It has been studied in several papers. In this paper, we extend a recent study, made on the coset leaders of the first order Reed-Muller codes, to two 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 and threshold functions (this second class being a generalization of the class of majority functions).