It has been established that the appropriate criteria for space-time trelli
s coded modulation (STTCM) design on slow Rayleigh fading channels are maxi
misation of the minimum rank and the minimum determinant of the distance ma
trices. It is demonstrated that when STTCM is used in systems with a large
product (>3) of the numbers of transmit and receive antennas. the design of
codes with maximum coding gain is governed by the minimum trace of the dis
tance matrices. A number of new codes based on the proposed design criterio
n have been constructed and shown to be superior to other known codes.