关键词: 平衡函数, 对称函数, 背包方程, 非平凡解

Abstract:

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-trivial 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.

Key words: balanced functions, symmetric functions, knapsack equation；non-trivial solutions