中文摘要：

线性复杂度和k错线性复杂度是度量密钥流序列的密码强度的重要指标.通过研究周期为2＂的二元序列线性复杂度,提出将k错线性复杂度的计算转化为求Hamming重量最小的错误序列.基于Games-Chan算法,讨论了线性复杂度为2^n的2^n周期二元序列的3错线性复杂度分布情况;给出了对应k错线性复杂度序列的完整计数公式,k=3,4.对于一般的线性复杂度为2^n-m的2^n周期二元序列,也可以使用该方法给出对应k错线性复杂度序列的计数公式.

英文摘要：

The linear complexity and the k-error linear complexity of a sequence have been used as important measures of keystream sequence strength. By studying linear complex-ity of binary sequences with period 2^n, it is proposed that the computing of k-error linear complexity should be converted to finding error sequences with minimal Hamming weight. Based on Games-Chart algorithm, 3-error linear complexity distribution of 2^n-periodic bi-nary sequences with linear complexity 2^n is discussed. For k = 3, 4, the complete counting functions on the k-error linear complexity of 2^n-periodic binary sequences with linear com-plexity 2^n are derived. Based on those results, the counting functions for the number of all 2^n-periodic binary sequences with given 3-error linear complexity can be obtained. Gener-ally, the complete counting functions on the k-error linear complexity of 2^n-periodic binary sequences with linear complexity 2^n - m can be obtained using a similar approach.