Boolean functions with two distinct Walsh coefficients
Boolean functions with two distinct Walsh coefficients
复制标题
DOI：
10.1007/s00200-011-0155-3
复制
发表时间：
2011-12
期刊：
影响因子：
--
通讯作者：
Ziran Tu;Dabin Zheng;Xiangyong Zeng;L. Hu
中科院分区：
文献类型：
--
作者：
Ziran Tu;Dabin Zheng;Xiangyong Zeng;L. Hu
除了仿射布尔函数和最大非线性（即弯曲）布尔函数之外，是否还有其他布尔函数具有两个不同的沃尔什系数？本文证明了具有两个不同沃尔什系数的布尔函数即是已知的两类仿射布尔函数和弯曲布尔函数，以及在x = 0时修改仿射布尔函数和弯曲布尔函数的值所得到的布尔函数。
Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions? This paper proves that all Boolean functions with exactly two distinct Walsh coefficients are just the two known classes of affine and bent Boolean functions and the Boolean functions obtained by modifying the value of affine or bent Boolean functions atx= 0.