4错线性复杂度的2n周期序列计数

Counting functions for 2 n-periodic binary sequences with 4-error linear complexity

k错线性复杂度是衡量序列密码稳定性的重要指标之一。给出求满足4错线性复杂度的2n周期序列计数的过程。把4错线性复杂度的研究分解为对关键错误线性复杂度的研究，再用方体理论和筛选法讨论关键错误线性复杂度，得到相应关键错误点（下降点）4错线性复杂度的取值形式，及此时二元序列精确计数公式。最后，归纳出4错线性复杂度所有的取值形式和计算出满足4错线性复杂度的序列计数。

The k-error linear complexity is one of the important measures for assessing the stability of sequence cipher. First, we presented the process of counting functions of 2n-periodic binary sequences with given 4-error linear complexity. Then we studied the critical error linear complexity via cube theory and sieve method. The possible values of the 4-error linear complexity of corresponding critical error point （descent point） were obtained and the number of sequences with given 4-error linear complexity of corresponding critical error point were es-tablished. Finally, we got the all the possible value forms of the 4-error linear complexity and the counting func-tions of 2n-periodic binary sequences.