2^n周期二元序列的2位置错误谱

2-Position error spectrum of linear complexity for 2^n-periodic binary sequences

K错线性复杂度描述了k个位置发生变化后序列的线性复杂度的最小值,反映了序列的稳定性。但k错线性复杂度不能全面反映序列的稳定性,所以对k位置错误谱进行了研究,加深对k错线性复杂度的理解,更好得反映序列的稳定性。一般认为k错线性复杂度低的序列是不稳定的,不适合作为密钥序列,但是有的序列只有在改变某些位置才会引起线性复杂度的下降,k位置错误谱描述了错误位置的不同对线性复杂度的影响。主要是研究周期为2n的二元序列,发现这类序列线性复杂度的2位置错误谱的一些特征。

K-error linear complexity of periodic sequences describes sequence＇ s stability, which is the minimum value of the sequences when k positions of the sequence are altered. But it has been found that k-error linear complexity can＇ t fully describe sequence＇ s stability. To understand more about the k-error linear complexity the k-position error spectrum which will describe the stability of sequences is anal- yzed. Generally speaking a sequence of low k-error linear complexity will be unstable, and it will be not fit for a cryptographic sequence. But some sequences＇ linear complexity will decline just when some special positions are altered. K-position error spectrum will describe how the differences of the positions influence the linear complexity. The 2^n -periodic binary sequences are mainly discussed, some characters of 2-position error spectrum are found.