The Linear Complexity Of Binary Generalized Cyclotomic Sequences Of Twice Odd Length

Pseudo-random sequences are widely used in ranging systems, global positioning sys-tems, spread spectrum communication systems, simulation, software testing and radar system; particularly, in cryptography. Different properties of sequences satisfy various ap-plied backgrounds. It is common that sequences have the properties of long period, large linear complexity, low and homogeneous distributions of autocorrelation values. However, linear complexity of sequences is paid more attention to secret communication systems and cryptography. In the paper, we investigate the construction and randomness analysis of some kinds of generalized cyclotomic sequences. We obtain main results as follows:(1)Based on Whiteman’s generalized cyclotomy, new binary generalized cyclotomic sequences of order two and length2pq have been constructed, the minimal polynomial and linear complexity of the proposed sequences have been determined. The result shows that the maximum is2pq, the minimum is2pq-(p+q-2) and the sequences are good from the linear complexity viewpoint; we take some examples for verifying conclusions.(2) Based on Whiteman’s generalized cyclotomy, new binary generalized cyclotomic sequences of arbitrary order and length2pm+1qn+1have been constructed, the formula of linear complexity of the proposed sequences has been determined. That,is, Meanwhile, we verifying conclusions by taking some examples.