Counting minimal generator matrices

Given a particular convolutional code C, we wish to find all minimal generator matrices G(D) which represent that code. A standard form S(D) for a minimal matrix is defined, and then all standard forms for the code C are counted (this is equivalent to counting special pre-multiplication matrices P(D)). It is shown that all the minimal generator matrices G(D) are contained within the `ordered row permutations´ of these standard forms, and that all these permutations are distinct. Finally, the result is used to place a simple upper bound on the possible number of convolutional codes