On cryptographic properties of the cosets of R(1, m)

We introduce a new approach for the study of weight distributions of cosets of the Reed-Muller code of order 1, Our approach is based on the method in troduced by Kasami in [1], using Pless identities. By interpreting some equ ations, we obtain a necessary condition for a coset to have a "high" minimu m weight. Most notably, we are able to distinguish such cosets which have t hree weights only. We then apply our results to the problem of the nonlinea rity of Boolean functions. We particularly study the links between this cri terion and the propagation characteristics of a function.