Im having troubles coping with encoders in other than controller normal form. Given for example this encoder (i/o is in binary) 
It has 2 physical states, because it has one memory and stores u_1+u_2 here (and it`s 0 or 1). Because $v_1 = u_1D + u_2D + u_1$, $v_2 = u_1D + u_2D + u_2$, I would call matrix \begin{pmatrix} 1+D & D \\ D & 1+D \end{pmatrix} produces generator matrix for the code given by the encoder. But the matrix has 4 abstract states (obvious since it looks at $u_1, u_2$ and their past separately) and the controllel normal form has also 4 states (corresponding to separating the branches) and thus is minimal. It is strange for encoder to have less physical states than its generator matrix has abstract states, isnt it?