  Detailed information about the weight distribution of a convolutional code is
given by the adjacency matrix of the state diagram associated with a controller
canonical form of the code. We will show that this matrix is an invariant of
the code. Moreover, it will be proven that codes with the same adjacency matrix
have the same dimension and the same Forney indices and finally that for
one-dimensional binary convolutional codes the adjacency matrix determines the
code uniquely up to monomial equivalence.
