Recently, weight divisibility results on resilient and correlation immune Boolean functions
have received a lot of attention. These results have direct consequences towards the upper
bound on nonlinearity of resilient and correlation immune Boolean functions of certain order.
Now the clear requirement in the design of resilient Boolean functions (which optimizes
Siegenthaler's inequality) is to provide results which attain the upper bound on nonlinearity.
Here we construct a 7-variable, 2-resilient Boolean function with nonlinearity 56. This solves …