首先给出了最优代数免疫布尔函数弹性阶的一个上界,并且证明了一类5元1阶弹性函数不是最优代数免疫函数,得到了最优代数免疫函数具有一阶弹性时可能的结构形式;在此基础上,给出了布尔函数代数免疫阶和弹性阶随着变元个数变化的一些结果,最后给出了一个5元1阶弹性的最优代数免疫布尔函数。
An upper bound of the resilience of Boolean functions with optimal algebraic immunity was proposed,proved that the algebraic immunity of a special family of 1st-resilience Boolean functions with five variables were not optimal,and demonstrated some possible structures of the 1st-resilience Boolean functions with optimal algebraic immunity.In addition,the relationships among the number of the variables,the algebraic immunity,and the resilient order were stidied.At last,a 1st-resilience Boolean function with five variables with optimal algebraic immunity are given.