The Research On Linear Complexity Of Generalized Cyclotomic Binary Sequences With Length N

Pseudorandom sequences have widely applications in many domains, including radar navigation systems, ranging systems, spread-spectrum communication systems, global positioning systems, CDMA systems, stream ciphers systems, etc. The linear complexity of sequences, the length of the shortest linear feedback shift register which generate the corresponding sequence, is one important indictor for measuring the randomness properties of cryptographic sequences. Cryptographic sequences must have large linear complexity to resist many attacks, according to BM algorithm.Based on a range of research methods and results, we determine the linear complexity of generalized cyclotomic binary sequences, of order two and four with length N. And based on Ding-generalized cyclotomy, by choosing some different characteristic sets we construct a new generalized cyclotomic sequence, of order four with length pq. The lower bound of linear complexity of the sequence is provided and show that such constructed sequence have balance property and is good sequence.