偶数元平衡对称布尔函数的构造与计数  

The Construction and Enumeration of Symmetric Balanced Boolean Functions with Even Number of Variables

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6期25-27,共3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个变量的背包方程的求解与解的计数,并且当n为偶数时,该背包方程存在2组平凡解.给出了当n为偶数时,这个背包方程有非平凡解的充分必要条件;提供了一种求非平凡解的方法;求出了当n=6k+2和n=4k2-2(k为正整数)时,这个背包方程的非平凡解.The construction and enumeration of symmetric balanced Boolean functions is equivalent to the solution and enumeration of the solution of one knapsack equation with n variables in the binary field. There exist two trivial solutions of this knapsack equation when is even. The necessary and sufficient condition under which there exist non-trivlal solutions of this knapsack equation was given when is even. A method for finding out the non-trivial solutions was also shown. Some non-trivial solutions of this knapsack equation were found out when and.

关 键 词：平衡函数 对称函数 背包方程 非平凡解 

分 类 号：TN911.22[电子电信—通信与信息系统]