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We propose a space-time coding strategy based on the use of families of matrices orthogonal in the trace of their product. The advantages of the proposed method are: i) possibility for symbol-by-symbol detection; ii) full diversity gain with respect to the noise; iii) full transmission rate, provided that the number of receive antennas is sufficiently higher than the number of transmit antennas; iv) direct extension to multiuser systems. The price paid for these advantages is the presence of ISI or multiuser interference (MUI). The method offers great flexibility in designing codes that provide the desired trade-off between BER, transmission rate and receiver complexity. We provide a theoretical analysis, supported by simulation results, showing how to balance transmission rate with BER, in the presence of (controllable) ISI. Finally, we generalize the method to the multiuser case.