On the symmetries and structure of trellis codes

We describe techniques from symbolic dynamics to determine the symmetry system of a trellis code. The construction starts with the partition permutation group, G, and enumerates short sequences over G under which the code is invariant. These sequences are then used to generate a graph. The process terminates when either the image of the symmetry graph is the entire code C (in which case C is known to be geometrically uniform), or the length of the generators exceeds a bound derived from the memory of C. As an example of using these techniques we analyze the V.34 codes