线性复杂度为2^n-2^m-1的2^n-周期二元序列的k-错线性复杂度

k-error linear complexity of 2n-periodic binary sequences with linear complexity 2n -2m -1

线性复杂度和k-错线性复杂度是研究流密码稳定性的两个重要概念。当改变序列某几位时不会使得序列的线性复杂度急剧减少,说明该序列的稳定性良好。运用Chan-Games给出了当k=4或5时,F2上固定线性复杂度为2n-2m-1的2n-周期二元序列的k-错线性复杂度所有可能值,LCk(s)=0或LCk(s)=2n-2m-2r+1+c,LCk(s)=2n-2r+1+c。这一结果对流密码稳定性的研究有重要的应用价值。

Linear complexity and k-error linear complexity are two important concepts to study the stability of the stream ci- pher. When a sequences changed some bit don＇ t lead to the linear complexity sharply reduce, so the sequences more stability. For a 2n-periodic binary sequence with linear complexity 2n - 2m - 1 on F2, and k = 4 or 5, this paper obtained all the possible values of ,the k-error linear complexity using Chan-Games algorithm, LCk （ s ） = 0 or LCk （ s ） = 2n - 2m - 2r ＋ l ＋ C, LCk （s） = 2n -2r＋1 ＋ c. The result has an imnortant application value for study the stability of stream cipher.