We study the notion of linear structure of a function defined from F-2(m) t
o F-2(n), and in particular of a Boolean function. We characterize the exis
tence of linear structures by means of the Fourier transform of the functio
n. For Boolean functions. this characterization can be stated in a simpler
way. Finally, we give some constructions of resilient Boolean functions whi
ch have no linear structure.