A lower bound on the 2-adic complexity of modified Jacobi sequence

Let $p,q$ be distinct primes satisfying $\mathrm{gcd}(p-1,q-1)=d$ and let $Di$, $i=0,1,\cdots,d-1$, be Whiteman's generalized cyclotomic classes with $Z{pq}^{{\ast}=\cup{i=0}{d-1}Di$.} In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets $D0^{\ast}=\sum{i=0}^{{\frac{d}{2}-1}D_{2i}$} and $D1^{\ast}=\sum{i=0}^{{\frac{d}{2}-1}D_{2i+1}$.} As an application, we determine a lower bound on the 2-adic complexity of modified Jacobi sequence. Our result shows that the 2-adic complexity of modified Jacobi sequence is at least $pq-p-q-1$ with period $N=pq$. This indicates that the 2-adic complexity of modified Jacobi sequence is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).