旋转对称布尔函数线性结构的2个公开问题

摘要

证明了代数次数为1n−的偶变元平衡旋转对称布尔函数不存在非零线性结构这个公开问题，给出了代数次数为2n−的奇变元旋转对称布尔函数不存在非零线性结构这个公开问题成立的充分条件和不成立的必要条件。%One open problem that the balanced rotation symmetric Boolean functions with degree n− on even number 1 of variables have no non-zero linear structure was proved. A sufficient and a necessary condition were respectively given when another open problem that the rotation symmetric Boolean functions with degree n− on odd number of varia-2 bles have no non-zero linear structure succeed or not.