n元m阶相关免疫对称函数的构造等价于方程sum C_(n-2)~iX_i from i=0 to (n-2)=sum C_(n-2)~iX_(i+1) from i=0 to (n-2)在二元域上的求解。通过对该方程及其等价方程解的关系讨论,给出了构造奇数元二阶相关免疫对称函数的算法。
Constructions of n-variable symmetric Boolean functions with second-order correlation-immunity is equivalent to solve the eqution sum C_(n-2)~iX_i from i=0 to (n-2)=sum C_(n-2)~iX_(i+1) from i=0 to (n-2) in the binary field. By discussing the relationship between the solutions of the equation and its equivalent equation, an algorithm of constructing odd-variable symmetric Boolean functions with second-order correlation-immunity is proposed.