Periodic Sequence Of Linear Complexity Stability Analysis

Stability of the linear complexity of the stream cipher is an important standard to scale the randomicity of a key sequence, k-trror linear complexity is a measurement to the stability of the linear complexity. Let s be a binary sequence, LCk(s) its k-error linear complexity for k > 0, and err1(s) ) the minimum value k such that LCk(s) < LC{s). The value of err1(s) for binary sequences with period 2" has been given by Kurosawa. In this paper, the k-error linear complexity of binary sequences with period 2" is discussed by use of the Hamming weight of polynomials. And the minimum value t with LC,(s) < LCr(s) for r = err(s) is obtained for a kind of binary sequences with period 2".Also in this paper, we studied the linear complexity of period sequences obtained from a binary period sequences by one symbol delete or one symbol insert. And we get the upper bound and lower bound of this kind of sequences by studying the form of the characteristic polynomial of these sequences.