The authors analyse a new topology for designing ring-TCM schemes over N-dimensional constellations. The squared free distance of these codes is optimised, thus optimisation is performed for AWGN channels. The generalised topology is studied for M-PSK and N-dimensional constellations. An improvement is obtained by using an N-dimensional constellation, in comparison with its M-PSK constellation counterpart. This improvement is more evident for higher level constellations.