Minimality and canonicity tests for rational generator matrices for convolutional codes

We derive computationally efficient minimality and canonicity tests for rational generator matrices for convolutional codes. The first set of tests are given in terms of easily obtained equivalent polynomial generator matrices and are suitable for small k and n. New tests are derived based on the scalar generator matrix G which are computationally more efficient for large k and n and small v. The application of these tests to generator matrices for (P)UM codes is studied. Finally, the results of O'Donoghue and Burkley (see Lecture Notes in Computer Science, vol.1365, p.258-65, 1997) are extended to the enumeration of minimal and canonical rational generator matrices.