Annihilator immunity of a bent function

Annihilator immunity and nonlinearity both are important properties of a Boolean function. Optimal values of these properties is desired but it is not possible as if we want optimal nonlinearity(bent functions), annihilator immunity and resiliency cannot be optimal. Similarly with maximum value of annihilator immunity, optimal value of nonlinearity and resiliency is not possible. So, we have constructed two different classes of desired Boolean functions, first class have bent functions(optimal nonlinearity) with sub-optimal bound of annihilator immunity, and in other one we have constructed Boolean functions having optimal bound of annihilator immunity with good bound of nonlinearity. In this paper, we have introduced a new method based on NSGA-II and achieved optimum value of annihilator immunity.