On $2k$-Variable Symmetric Boolean Functions With Maximum Algebraic Immunity $k$
Hui Wang, Jie Peng, Yuan Li, Haibin Kan · IEEE Transactions on Information Theory · 2012
Given a positive even integer n, it is found that the weight distribution of any n-variable symmetric Boolean function with maximum algebraic immunity (AI) n/2 is determined by the binary expansion of n . Based on the foregoing, all n-variable symmetric Boolean functions with maximum AI are constructed. The amount is (2 wt(n)+1)2[log2n].