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Space-frequency (SF) codes that exploit both spatial and frequency diversity can be designed using orthogonal frequency division multiplexing (OFDM). However, OFDM is sensitive to frequency offset (FO), which generates intercarrier interference (ICI) among subcarriers. We investigate the pair-wise error probability (PEP) performance of SF codes over quasistatic, frequency selective Rayleigh fading channels with FO. We prove that the conventional SF code design criteria remain valid. The negligible performance loss for small FOs (less than 1%), however, increases with FO and with signal to noise ratio (SNR). While diversity can be used to mitigate ICI, as FO increases, the PEP does not rapidly decay with SNR. Therefore, we propose a new class of SF codes called ICI self-cancellation SF (ISC-SF) codes to combat ICI effectively even with high FO (10%). ISC-SF codes are constructed from existing full diversity space-time codes. Importantly, our code design provide a satisfactory tradeoff among error correction ability, ICI reduction and spectral efficiency. Furthermore, we demonstrate that ISC-SF codes can also mitigate the ICI caused by phase noise and time varying channels. Simulation results affirm the theoretical analysis.