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）.
出处
《北京邮电大学学报》
EI
CAS
CSCD
北大核心
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)
关键词
平衡函数
对称函数
严格雪崩准则
背包方程
balanced functions
symmetric functions
strict avalanche criterion
knapsack equation
