  Perfect space-time codes were first introduced by Oggier et. al. to be the
space-time codes that have full rate, full diversity-gain, non-vanishing
determinant for increasing spectral efficiency, uniform average transmitted
energy per antenna and good shaping of the constellation. These defining
conditions jointly correspond to optimality with respect to the Zheng-Tse D-MG
tradeoff, independent of channel statistics, as well as to near optimality in
maximizing mutual information. All the above traits endow the code with error
performance that is currently unmatched. Yet perfect space-time codes have been
constructed only for 2,3,4 and 6 transmit antennas. We construct minimum and
non-minimum delay perfect codes for all channel dimensions.
