  Let $p,q$ be distinct primes satisfying $\mathrm{gcd}(p-1,q-1)=d$ and let
$D_i$, $i=0,1,\cdots,d-1$, be Whiteman's generalized cyclotomic classes with
$Z_{pq}^{\ast}=\cup_{i=0}^{d-1}D_i$. In this paper, we give the values of Gauss
periods based on the generalized cyclotomic sets
$D_0^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i}$ and
$D_1^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i+1}$. 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).
