中文摘要：

k-错线性复杂度是度量密钥流序列的密码强度的一个重要指标．为了更好地刻画和研究序列的随机性，研究了周期为2^n的二元序列s_的k-错线性复杂度（Lct（s_））的分布情况，讨论了满足LCk（s_）-LC（s_＋e_）条件下的k-错误序列e的分布情况．基于Games-Chan算法，通过将k-错线性复杂度的计算转化为求Hamming重量最小的错误序列的方法，给出了线性复杂度小于2^n的2^n周期二元序列的部分4-错误序列的计数公式．

英文摘要：

The k-error linear complexity of a sequence has been used as one of the important measure of keystream strength. In order to better depict and study randomicity of sequences, the k-error sequences （e_） distribution that corresponds with LCk （s_）= LC （s_＋ e_） is discussed by studying the distribution of k- error linear complexity of binary sequences （s） with period 2^n. Based on Games-Chan algorithm,it is proposed that the computation of k-error linear complexity should be converted to finding error sequences with minimal Hamming weight. For k =4, some the counting functions on the k-error sequences of 2^n-pe- riodic binary sequences with linear comolexitv less than 2^n are derived.