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We derive the performance union bound of space-time trellis codes in orthogonal frequency division multiplexing system (STTC-OFDM) over quasistatic frequency selective fading channels based on the distance spectrum technique. The distance spectrum is the enumeration of the codeword difference measures and their multiplicities by exhausted searching through all the possible error event paths. Exhaustive search approach can be used for low memory order STTC with small frame size. However with moderate memory order STTC and moderate frame size the computational cost of exhaustive search increases exponentially, and may become impractical for high memory order STTCs. This requires advanced computational techniques such as genetic algorithms (GAs). A GA with sharing function method is used to locate the multiple solutions of the distance spectrum for high memory order STTCs. Simulation evaluates the performance union bound and the complexity comparison of nonGA aided and GA aided distance spectrum techniques. It shows that the union bound give a close performance measure at high signal-to-noise ratio (SNR). It also shows that GA sharing function method based distance spectrum technique requires much less computational time as compared with exhaustive search approach but with satisfactory accuracy.