一种新的平衡对称布尔函数的构造和计数方法

摘要

平衡对称布尔函数的构造与计数等价于二元域上某个含有n个变量背包方程的求解与解的计数.对平衡对称布尔函数的构造方法进行研究,通过寻找特定的组合恒等式来化简特定元背包方程,进而求出特定元背包方程的部分非平凡解,并对部分平衡对称布尔函数的计数下界作了较好的改进.%The construction and enumeration of symmetric balanced Boolean functions are equivalent to the solution and enumeration of the solutions of one knapsack equation with n variables in the binary field. In this paper,we study the method of constructing a symmetric balanced Boolean function. With finding the specific combination identity,we can find the special variable knapsack equation,and then obtain the partial non-trivial solutions of the specific variable knapsack equation. The partial lower bound of the symmetric balanced Boolean function is improved.