Phase coding is one of the early methods for pulse compression. In this talk, we extend the class of phase coded waveforms to a new class of signals coded by finite Gabor systems. Our motivation is based on two facts. First, it is not difficult to compute the ambiguity function of the new signals. Second, these signals lead to some ambiguity function performances which cannot be reached by considering the class of phase coded waveforms alone. To prove this, we introduce a family of linear mappings transforming phase coded waveforms on waveforms coded by finite Gabor systems and leading to ambiguity functions with reduced sidelobes.