给定k-错线性复杂度的2~n-周期二元序列条数及Matlab程序

The Number of 2~n-period Binary Sequences of a Given k-error Linear Complexity and Matlab Program

k-错线性复杂度是流密码研究的重要指标,当序列中的几位出错不会使序列的线性复杂度急剧下降,这说明该序列的稳定性良好.运用Chan-Games算法给出了满足LC2 n,4(s)=0、LC2 n,4(s)=2n-2m-2r+1+c的序列条数分别为(2m-1)2×24n-2m-6、22 n-2 m-2 r+1+c+2r-1,(2≤r≤m-1、1≤c≤2r-2),以及利用Matlab程序给出满足这些条件的所有序列.这一结论对于研究流密码稳定性有一定的应用价值.

k-error linear complexity is an important indicator of stream ciphers research. When some are wrong in a sequence,which will not lead to the sharp reduction of linear complexity,so the sequences are more stable. In this paper,using Chan-Games algorithm gives the number of sequences with LC2 n,4（s） = 0、LC2n,4（s） = 2n-2m-2r ＋ 1＋ c,respectively（2m-1）2× 24n-2m-6、22n-2m-2r ＋ 1＋ c ＋ 2r-1,（2≤r≤m-1、1≤c≤2r-2）,and using Matlab program it gives all sequences that satisfy these conditions. The result has an important application value for studying the stability of stream cipher.