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中文摘要：
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=4k^2-2（k为正整数）时，这个背包方程的非平凡解．
英文摘要：
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.
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