Summary form only given, as follows. New trellis codes over GF(q) are presented for one- and two-dimensional Euclidean spaces. A closed-form expression is derived for the squared free Euclidean distance and for the asymptotic coding gain for the combined form of M-PAM with convolutional codes with one and two memory elements. The corresponding generator matrices for a class of these codes are also presented. Curves showing the asymptotic behavior are provided. By use of the solutions of the diophantine equation (set partitioning) and the generalized minterm technique associated with the concept of Latin square, new trellis codes are tabulated for the combined form of QAM and convolutional codes with one memory element. 6768