On maximally nonlinear and extremal balanced Boolean functions
Michel Mitton · Journal of Discrete Mathematical Sciences and Cryptography · 2002
We prove a new sufficient condition for a Boolean function to be extremal balanced or maximally nonlinear, in odd or even dimension. Under this condition, we deduce the balanced covering radius ρB(n) and the covering radius ρ(n). We prove some general properties about maximally nonlinear or extremal balanced functions. Finally, an application to even weights Boolean functions is given.