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In this letter, we propose two full-rate space-time-frequency trellis code (STFTC) designs for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The first proposal based on rotating constellation is called extended super-orthogonal STFTC (Ex-SOSTFTC). The second proposal, called Quasi-Orthogonal STFTCs (QOSTFTCs), combines set partitioning and the structure of quasi-orthogonal space-frequency designs in a systematic way. In addition to spatial diversity, the proposed codes provide multipath diversity and achieve high-coding gain over a frequency selective fading channel. Simulation results show the proposed codes significantly outperform the existing STFTC designs.