  We prove that an overcomplete Gabor frame in $ \ell^2(\mathbf Z)$ by a
finitely supported sequence is always linearly dependent. This is a particular
case of a general result about linear dependence versus independence for Gabor
systems in $\ell^2(\mathbf Z)$ with modulation parameter $1/M$ and translation
parameter $N$ for some $M,N\in \mathbf N,$ and generated by a finite sequence
$g$ in $\ell^2(\mathbf Z)$ with $K$ nonzero entries.
