Some important results:

  1. Rate one generalized complex orthogonal designs do not exist for more than two transmit antennas
  2. The rate of a generalized complex orthogonal design cannot exceed R = 3/4 for more than two antennas
  3. Rate half, R = 0.5, generalized complex orthogonal designs exist for any number of transmit antennas 
  4. For a generator matrix for a given rate and number of antennas, a generator matrix of same rate for number of tranmist antennas less by one can be obtained by simply removing one column.