Abstract:Some properties of autocorrelation coefficient and cross-correlation coefficient are given. The restricted relationship among n(n variables, wt(f) (the Hamming weight of Boolean function f (x) and t (t-th propagation criteria) was derived, then a lower bound on the sum-of-squares of any Boolean functions with Hamming weight k is concluded. Finally, the results generalized a upper bound on nonlinearity of Boolean function only depending on Hamming weight. This paper improved known results.
周 宇; 王维琼; 肖国镇. Hamming重量为k的布尔函数的全局特征和非线性度[J]. 电子与信息学报, 2009, 31(2): 435-438 .
Zhou Yu①; Wang Wei-qiong①②; Xiao Guo-zhen①. Global Avalanche Characteristics and Nonlinearity of Boolean Function with the Hamming Weight k. , 2009, 31(2): 435-438 .