Autocorrelation of the Two-prime Sidelnikov Sequence

Brandsttter et al. (2011) combined the concepts of the two-prime generator and Sidelnikov sequence to define a new sequence called two-prime (p, q) Sidelnikov 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 Sidelnikov 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?tters bound O((p+q)/2), besides, the bound O((p q) 1/2) in theorem 4 are tighter than the Brandsttters bound O((p+q) /2+(p q) 1/2) when p q or q p.