关于旋转对称布尔函数线性结构的几点注记
doi: 10.3724/SP.J.1146.2012.00193
The Notes on the Linear Structures of Rotation Symmetric Boolean Functions
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摘要: 该文研究了旋转对称布尔函数(RSBF)的线性结构特征，讨论了RSBF的代数次数与线性结构点之间的关系。证明了代数次数为n-1且平衡的偶数元RSBF不存在非全0的线性结构点这个公开问题。给出了自共轭轨道的计数公式，并以此计算了以全1向量为其线性结构点的RSBF的个数。Abstract: In this paper, the linear structure of Rotation Symmetric Boolean Functions (RSBF) is studied. The relationship between the degree and the existence of linear structures in RSBFs is investigated. The open problem that an-variable RSBF being balanced and of degree n-1 has no linear structure except the all-zero vector is proved. A formula for enumerating the self-conjugate orbits is presented. By this formula, the number of RSBFs, which have no linear structure except all-one vectors, is obtained.
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