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In this paper, we propose a novel class of Space-Frequency and Space-Time-Frequency block codes based on Quasi-Orthogonal designs, over a frequency selective Rayleigh fading channel. The proposed Space-Frequency code is able to achieve rate-one and full space and multipath diversity gains available in the MIMO-OFDM channel. As simulation results demonstrate, the code outperforms the existing Space-Frequency block codes in terms of bit error rate performance. By coding across the three dimension of space, time and frequency, we propose a Quasi-Orthogonal Space-Time-Frequency code that is capable of achieving rate-one and exploiting all of the spatial, multipath and temporal diversity gains offered by the channel. In case of a channel which is quasi-static over adjacent OFDM symbol durations, we propose a Space-Time-Frequency code that benefits from a reduced maximum likelihood decoding complexity.