Can i use Babai algorithm in q-ary lattice Let's assume we have the q-ary lattice 

$$ \mathcal{L}_q({\bf A})=\{ {\bf z}\in \mathbb{Z}^{n} : \exists {\bf s}\in \mathbb{Z}^{n}_{q} \ , \ {\bf z}={\bf A s}^{T} \mod q   \},$$

where ${\bf A}\in \mathbb{Z}^{n\times n}_{q}$.

My question is, can I use the Babai's algorithm with input the matrix ${\bf A}$ and a target vector ${\bf t}\in \mathbb{Z}_{q}^{n}$,  to find a close lattice vector to ${\bf t}$ ?
No, you can't.

Babai's Nearest Plane Algorithm is supposed to receive a basis of the lattice, and $\mathbf{A}$ is not the basis of the modular lattice that it spans. If you give Babai's algorithm the matrix ${\bf A}$, it will work over the lattice $ \mathcal{L}({\bf A}) := \{ {\bf A}{\bf x} : {\bf x} \in \mathbb{Z}^n  \}$ instead of $\mathcal{L}_q({\bf A}) $. Therefore, it will probably output wrong answers.

For instance, if you take a vector $\mathbf{t} = (q, q, ..., q)$, then $\mathbf{t} \in \mathcal{L}_q({\bf A})$, therefore, Babai's algorithm must output $\mathbf{t}$ itself. But it is likely that $\mathbf{t} \not \in \mathcal{L}({\bf A})$, so, Babai's algorithm will output some vector different from ${\bf t}$.