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We introduce a novel space-time coding scheme, called space-time cyclic-delay coding (STCDC), for multiple input multiple output orthogonal frequency-division multiplexing (MIMO-OFDM) systems over frequency-selective fading channels. The scheme exploits the redundancy introduced by channel coding. The transmitter antennas send the cyclically delayed copies of OFDM symbols, and the receiver uses the maximum likelihood estimation method to estimate the transmitted sequence. We show that STCDC-OFDM can achieve the maximum diversity, which is the product of the number of transmitter antennas (Nt), the number of receiver antennas (Nr) and the channel length (L), if the error control code has at least a free distance of NtL. Compared with the existing space-time coding and space-frequency coded MIMO-OFDM techniques, the proposed scheme has the advantages of being independent from the number of transmit antennas and having a lower implementation complexity.