机构地区: 信息安全国家重点实验室
出 处: 《系统科学与数学》 2004年第4期479-487,共9页
摘 要: Walsh谱只有3个值:0,±2m+2,且同时达到代数次数上界n-m-1和非线性度上界2n-1-2m+1的n元m阶弹性布尔函数(m>n/2-2)称为饱和最优函数(saturatedbest简写为SB).本文将给出关于SB函数非零谱值位置分布的一个性质,利用这一性质我们给出构造非线性度为56的4次7兀2阶弹性布尔函数的一种方法. The n-variable and m-resilient (m > n/2 - 2) Boolean functions which have three valued Walsh spectra: 0,±2m+2, and achieve both the upper bound on nonlinearity 2n-1-2m+1 and the upper bound on algebraic degree n - m - 1 are called saturated best (SB in short). A property about the distribution of the positions where a SB function has nonzero spectra is given in this note. We use this property to find a new approach to construct 7-variable and 2-resilient functions with degree 4 and nonlinearity 56.