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This paper proposes novel space-time-frequency (STF) coding for multi-antenna orthogonal frequency-division multiplexing (OFDM) transmissions over frequency-selective Rayleigh fading channels. Incorporating subchannel grouping and choosing appropriate system parameters, we first convert our system into a set of group STF (GSTF) systems. This enables simplification of STF coding within each GSTF system. We derive design criteria for STF coding and exploit existing ST coding techniques to construct both STF block and trellis codes. The resulting codes are shown to be capable of achieving maximum diversity and coding gains, while affording low-complexity decoding. The performance merits of our design are confirmed by corroborating simulations and compared with existing alternatives.