中文摘要：

通过将周期为2n的二元序列的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,研究序列的k-错线性复杂度的分布情况,讨论了序列不同k-错线性复杂度条件下对应的k-错误序列的分布情况。基于Games-Chan算法,给出了线性复杂度小于2n的2n周期二元序列的4-错线性复杂度分别为2n-1-（2m＋2j）和2n-1-（2m＋2j）＋x情况下的4-错误序列的计数公式。同时,给出实例并使用计算机进行验证。

英文摘要：

By studying k-linear complexity of binary sequences with period 2^n,it is proposed tion of k-error linear complexity should be converted to finding error sequences with minimal that the computa- Hamming weight. Then the k-error sequences distribution that corresponds with the k-error linear complexity of sequence is dis- cussed. Based on Games-Chan algorithm, for k=4, the counting function on the k-error sequences of 2^n-periodic binary sequences whose linear complexity less than 2^n and the k-error linear complexity are 2^n-1-（2^n＋2^i） and 2^n-1- （2^n＋2^i）＋x is derived. Examples are presented to illustrate the results and checked by computer.