Autocorrelation of the Two-prime Sidel’nikov Sequence
Yue Zhao① Gao Jun-tao①② Xie Jia①
①(The State Key Laboratory of Integrated Services Network, Xidian University, Xi’an 710071, China)
②(Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China)
Abstract：Brandstätter et al. (2011) combined the concepts of the two-prime generator and Sidel’nikov sequence to define a new sequence called two-prime (p, q) Sidel’nikov sequence, and analyzed the balance, the autocorrelation, the correlation measure and the linear complexity profile of the sequence. They showed that this sequence has many nice pseudorandom properties. With the help of the Legendre symbol in number theory and the exponential sums in finite field, this paper investigates the autocorrelation of the two-prime Sidel’nikov sequence with d=gcd(p, q)=2. Three theorems are got about the autocorrelation functions. The detailed comparison results show that the bounds O(q1/2) and O(p1/2) on the autocorrelation function in theorem 2 and theorem 3 are tighter than the Brandst?tter’s bound O((p+q)/2), besides, the bound O((pq) 1/2) in theorem 4 are tighter than the Brandstätter’s bound O((p+q) /2+(pq) 1/2) when p >>q or q >>p.
2013, Vol. 35 
