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The pairwise-error probability upper bounds of space-time codes (STCs) in independent Rician fading channels are derived. Based on the performance analysis, novel code design criteria for slow and fast Rayleigh fading channels are developed. It is found that, in fading channels, the STC design criteria depend on the value of the possible diversity gain of the system. In slow fading channels, when the diversity gain is smaller than four, the code error performance is dominated by the minimum rank and the minimum determinant of the codeword distance matrix. However, when the diversity gain is larger than, or equal to, four, the performance is dominated by the minimum squared Euclidean distance. Based on the proposed design criteria, new codes are designed and evaluated by simulation.