旋转对称布尔函数线性结构的2个公开问题  

Two open problems about the liner structure of rotation symmetric Boolean functions

作　　者：赵亚群[1,2] 李旭 

机构地区：[1]信息工程大学四院,河南郑州450002 [2]信息工程大学数学工程与先进计算国家重点实验室,河南郑州450002

出　　处：《通信学报》2013年第3期171-174,共4页Journal on Communications

基　　金：国家自然科学基金资助项目(61072046)~~

摘　　要：证明了代数次数为n 1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n 2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 - 1 on even number 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- 2 on odd number of vari- ables have no non-zero linear structure succeed or not.

关 键 词：布尔函数 旋转对称 线性结构 代数次数 

分 类 号：TN918.1[电子电信—通信与信息系统]