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Multiple input multiple output (MIMO) communication systems with orthogonal frequency division multiplexing (OFDM) modulation have a great potential to play an important role in the design of the next-generation broadband wireless communication systems. In this paper, we address the problem of performance analysis and code design for MIMO-OFDM systems when coding is applied over both spatial, temporal, and frequency domains. First, we provide an analytical framework for the performance analysis of MIMO-OFDM systems assuming arbitrary power delay profiles. Our general framework incorporates the space-time and space-frequency (SF) coding approaches as special cases. We also determine the maximum achievable diversity order, which is found to be the product of the number of transmit and receive antennas, the number of delay paths, and the rank of the temporal correlation matrix. Then, we propose two code design methods that are guaranteed to achieve the maximum diversity order. The first method is a repetition coding approach using full-diversity SF codes, and the second method is a block coding approach that can guarantee both full symbol rate and full diversity. Simulation results are also presented to support the theoretical analysis.