Minimal trellises for linear block codes and their duals

We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity for a fixed permutation of the code. We examine constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code. We identify the primitive structures that can appear in a minimal trellis and relate this to those for the minimal trellis of the dual code.