Constructing Method Of Optimum Algebraic Immunity Boolean Function

Carlet C by using the relationship between the Hamming weight and the Boolean function's algebra number, through the Boolean function in certain affine subspace's limit, gave that there is no low-annihilator of a sufficient condition for a Boolean function.In this paper, we use this thought and give a more intuitive method of construction of the even number of variables function with optimum algebraic immunity, and extend the conclusions given by Carlet C. The even number of variables function with optimum algebraic immunity given by this method has more number and clearer structure,we improved the method of construction of the odd number of variables function with optimumalgebraic immunity proposed by Carlet, obtained the conditions which can reach maximum and minimum of constructed functions' number, given a maximum number of exchange elements method for the constructed optimum algebraic immunity Boolean functions, so that the constructed functions have a greater difference from majority functions and symmetric functions.