This paper proposes high-rate full-diversity space-frequency trellis code (SFTC) designs, which achieve the full diversity advantage at high transmission rate, for frequency selective fading channels. The proposed SFTC are derived based on the concept of concatenated space-time block code (STBC) and multiple trellis coded modulation (MTCM) encoder constructions. The existing SFTC designs only provide small frequency diversity and coding gain advantages for the case in which the channel delay spread is small. Here, the proposed codes achieve larger coding gain and frequency diversity advantages than the codes ob-tained from the existing designs. Simulation results show that the proposed designs signicantly outper-form the conventional designs. Not only is a class of trellis codes proposed in this paper, but we also address the design of rate-one full-diversity space-frequency block code (SFBC) for frequency selective fading channels. The newly designed SFBC outper-forms the existing SFBCs, including the conventional rate-one and conventional rate-two SFBCs. The performance gain of the proposed SFBC is mathematically proven and also illustrated via simulation results.