中文摘要：

文章指出了论文“A wide family of nonlinear filter functions with a large linear span”存在的问题，给出一个反例，同时得到如下结论：设a_是F2上以f（x）为极小多项式的n级m-序列，a为f（x）的一个根，a^δ为F2^n在F2上的正规元，1≤δ〈2^n-1。设2≤k≤n-2，令Гδ，k={xδxδ2^dxδ2^2d…xδ2^（k-1）d＋G（Gx0，x1，…，x2^n-2）｜deg（G（x0,x1,…,x2^n-2））〈k，gcd（d，n）=1}，则以Гδ，k中的任意布尔函数作为非线性过滤函数作用在a_上得到的输出序列线性复杂度下界为（n k）。记F2^n在F2上的正规元的数量为v（n），则集合{xδxδ2^dxδ2^2d…xδ2^（k-1）d｜1≤δ〈2^n-1，a^δ为F2^n在F2上的正规元，d〈n，gcd（d，n）=1}中互异函数的个数为φ（n）·v（n）／2。

英文摘要：

In this paper, we point out the problems in ＂A wide family of nonlinear filter functions with a large linear span＂, give a counterexample, and get the following conclusions： Let a he a binary m-sequence of degree n with minimal polynomial f（x）. Let a he a root of f（x）, and a^δ a normal element in F2^n over F2 ,where 1≤δ〈2^n-1. Let k he a positive integer and 2≤ k ≤ n - 2. Set Гδ,k={xδxδ2^dxδ2^2d…xδ2^（k-1）d＋G（Gx0,x1,…,x2^n-2）｜deg（G（x0,x1,…,x2^n-2））〈k,gcd（d,n）=1} ,then forany F∈Гδ,k ,the linear complexity of the filtered sequence produced by F acting on a is lower hounded by （n k）. Denote the number of normal elements in F2^n over F2 by v （ n）, then the number of different elements in {xδxδ2^dxδ2^2d…xδ2^（k-1）d｜1≤δ〈2^n-1, a^δ is a normal element of F2^n over F2, d 〈 n, gcd（ d, n ） =1} is φ（n） ·v（n）/2.