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Using two transmit antennas and one receive antenna, Alamouti's schemes (1998) provide the maximum possible diversity gain with a maximum likelihood detector. In addition to diversity gain, this paper maximizes the coding gain using the minimum of the determinants of the code difference matrices. In order to achieve the maximum coding gain on a Rayleigh fading channel, a trellis code is designed to maximize the free Euclidean distance. Trellis-coded modulation is combined with Alamouti's schemes to provide additional coding gain. The design criteria of trellis coded modulation is based on Radon-Hurwitz matrices. Based on these criteria, new space-time trellis coded QPSK schemes are designed and shown to achieve good performance relative to space-time block codes. The performance of this code is evaluated through computer simulation.