H布尔函数的相关免疫性与重量的关系

摘要

将布尔函数的导数和与导数一起便可直接明确刻画布尔函数的重量而定义的e-导数一起作研究工具,深入到布尔函数取值的内部结构中去,讨论了在H布尔函数存在的一个大重量范围内,所有不同重量的H布尔函 数的一阶、任意m阶相关免疫函数存在与否的问题.对存在m阶相关免疫性的H布尔函数,它的相关免疫阶数m与维数n的具体关系,以及m的最大值问题.给出了m阶相关免疫H布尔函数只存在于2种重量的H布尔函数中,其相关免疫阶数m的最大值为n-2,以及其余重量的H布尔函数中不存在二阶以上(包括二阶)相关免疫函数等一系列结果.同时,也给出了一些判断布尔函数相关免疫性的方法.%The Boolean function derivative and e-derivative which together with the derivative so that the weight of Boolean functions can be directly clear characterized and defined as the tools for research and deep into the internal structure of Boolean function value, to discuss a large range in which the H-Boolean functions exist, the issue of whether all different weights of first-order and m-order H Boolean functions exist. For H Boolean functions with m-order correlation immunity, the relationship between its correlation immune order m and dimension n, and the maximum problem of m. Gives the m-order correlation immune H Boolean function exists only in the H Boolean function that with two kinds of weight. The maximum value of correlation immune m is n-2, and the rest of the weight of H Boolean function does not exist above the second-order (including the second-order) correlation immune ruction and a series of results.