Perfect Space-Time Codes for Any Number of Antennas

In a recent paper, perfect (n x n) space-time codes were introduced as the class of linear dispersion space-time codes having full rate, non-vanishing determinant, a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n2 dimensions and uniform average transmitted energy per antenna. Consequence of these conditions includes optimality of perfect codes with respect to the Zheng-Tse Diversity-Multiplexing Gain Tradeoff (DMT), as well as excellent low-SNR performance. Yet perfect space-time codes have been constructed only for 2; 3; 4 and 6 transmit antennas.