In this paper, the generation of 16-QAM and 64-QAM space-time trellis codes (STTCs) for several transmit antennas is considered. The main problem with an exhaustive search is the important time to find the best 2 2n -QAM STTCs, especially for great values of n and for great numbers of transmit antennas. In order to reduce this search time, an efficient method must be used to generate optimal 2 2n -QAM STTCs. Thus, a new method based on the decomposition of the Euclidean distance between 2

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... rds is proposed to design the optimal STTCs. Thanks to this new method, the first 16-QAM STTCs with more than 2 transmit antennas and the first 64-QAM STTCs with 2 and 3 transmit antennas are proposed. The performance of these new codes is evaluated by simulation.