Abstract: Using the derivative of Boolean functions and custom e-derivative as a research tool,we discussed the issue of algebraic immunity of H Boolean function with correlation immunity and weight of 2n－1+2n－2 which meets the strict avalanche criterion. We got the optimal algebraic immunity function and its construction method of these functions with odd(n≥17)variables and even(n≥16)variables and gave the construction method of algebraic immunity function with n variables that the algebraic immunity order is AI(f)≥8,also gave the method of solving the annihilator and the minimum algebraic degree annihilators and the derivative relations of annihilator and the Boolean function．The derivative of the Boolean function and the e-derivative defined with derivative can directly and explicitly depict the weight of the Boolean functions as research tools,in-depth to the internal structure of the value of the Boolean function.

Key words: H Boolean function,Correlation immune,Subfunction,Optimal algebraic immunity,Algebraic immunity order