平衡对称布尔函数的构造与计数  

The Construction and Enumeration of Symmetric Balanced Boolean Functions

作　　者：莫骄[1] 温巧燕[1] 

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《北京邮电大学学报》2006年第5期15-18,共4页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(60373059);教育部博士点基金项目(20040013007)

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.求出了当n为奇数时这个背包方程的1个解集合S以及S中所有解的个数,给出了这个背包方程存在其他解(即不包含于集合S的解)的充分必要条件,提出了1种求其他解的方法.求出了当n为6k+2(k为正整数)时这个背包方程的部分解.The construction and enumeration of symmetric balanced Boolean functions is equivalent to the solution and enumeration of the solutions of one knapsack equation with n variables in the binary field. A set S of solutions of this knapsack equation and the number of the elements in S was found when n is odd. The necessary and sufficient condition, under which other solutions（out of the set S） of this knapsack equation existed, was obtained. A method for finding out the solutions out of the set S was also given. Part of solutions of this knapsack equation were gotten when n = 6k ＋ 2 （k is positive integer）.

关 键 词：平衡函数 对称函数 严格雪崩准则 背包方程 

分 类 号：TN911.22[电子电信—通信与信息系统]