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The authors address the problematic issues in generating space-time trellis codes, and propose novel methods for reducing the exponentially growing full code search. It is proved that by exploiting the symmetry in QAM and PSK constellations, together with the modulo operation in the encoder, the number of possible combinations in the generator matrix can be halved when performing a full search to obtain optimal codes. It is also shown that for a fixed set of columns in the generator matrix, interchanging columns yields identical results, hence reducing the full code search by the factorial of the number of transmit antennas. Furthermore, the existing sub-optimal (but fast) method for obtaining codes is investigated and results from this method are compared with those obtained from the two proposed methods. Using the suggested methods, novel space-time codes for both slow and fast fading environments are generated and their performance is evaluated through frame error probabilities obtained by simulation.