周期为2^n的二元序列的整体稳定性

讨论周期为2^n的二元序列k-错误线性复杂度问题。周期为2^n的二元序列线性复杂度严格大于2^n-1。从二元周期序列的整体稳定性开始给出最小的k，使得全体周期为2^n的二元序列中至少有一半序列的k-错误线性复杂度不大于2^n-1。对全体周期为2^n的平衡序列和非平衡序列分别进行研究，给出相应最小的k。

Entire Stability of Binary Sequences with Period 2n

This paper studies the k-error linear complexity of binary sequences with period 2n.It is well known that the linear complexity of binary sequences with period 2n is strictly larger than 2n-1.Form the entire stability of binary periodic sequences,the minimal value k is given for which there are at least half of the sequences with period 2n have k-error linear complexity not larger than 2n-1.The minimal value k is studied for balanced sequences and imbalanced sequences with period 2n respectively.