Weightwise Perfectly Balanced Functions and Nonlinearity

In this article we realize a general study on the nonlinearity of weightwise perfectly balanced (WPB) functions. First, derive upper and lower bounds from class functions for all n. Then, give construction that allows us to provably provide WPB with as low $$2^{n/2-1}$$ high nonlinearity, at least $$2^{n-1}-2^{n/2}$$ . We concrete examples in 8 16 variables given by construction. experimentally obtain reaching 116 which corresponds bound Dobbertin’s conjecture, it improves upon maximal recently obtained genetic algorithms. Finally, distribution over set examine exact $$n=4$$ an algorithm estimate distributions $$n=8$$ 16, together results our experimental studies 16.