1 Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables ∗
Weiguo Zhang, Xiao Guo-zhen · 2009
In this paper, a primary construction of nonlinear resilient functions is described. We use disjoint spectra functions on a small number of variables to construct an almost optimal resilient function on a large even number of variables. It is shown that given any m, one can construct infinitely many n-variable (n even), m-resilient functions with nonlinearity> 2 n−1 − 2 n/2. A large class of highly nonlinear resilient functions which were not known are obtained. We then propose one method to optimize the degree of the constructed functions. Lastly, we give an improved version of our main construction.