Linear independenee of Gabor systems in finite dimensional vector spaces

We discuss the linear independence of systems of m vectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector. Such systems are called Gabor systems. When n is prime, we show that there exists an open, dense subset with full-measure of such generating vectors with the property that any subset of n vectors in the corresponding full Gabor system of n(2) vectors is linearly independent. We derive consequences relevant to coding, operator identification and time frequency analysis in general.