The theory of group codes simplifies the construction of good rotation
ally invariant trellis codes for the additive white Gaussian noise cha
nnel. New geometrically uniform trellis codes, with spectral efficienc
y 3 bits/2D, based on multidimensional L x 16-PSK constellations in 4,
6, and 8 dimensions, obtained by group trellis codes over nonbinary g
roups of the kind Z(16)(L), are presented. Most of the codes improve,
in terms of asymptotic gain and rotational invariance, the best codes
known so far in the literature.