if and only if $0\notin\{h_{0,1}, h_{0,2},h_{1,1},h_{1,2}\}$ and $h_{1,1}h_{0,2}-h_{1,2}h_{0,1}\neq 0$.

 \
A $(2,1,1)$ convolutional code is MDP if and only if it is complete MDP. Thus, the statements of the preceding theorem are also true for $(2,1,1)$ reverse convolutional codes and $(2,1,1)$ complete MDP convolutional codes.

 \
It is easy to the that the conditions on the parity-check matrix of the preceding remark are also sufficient to get a complete (and hence also a reverse) MDP convolutional code.

At the end of this subsection, we want to compute the probability of a $(2,1,1)$ MDP convolutional code under the condition that the code is non-catastrophic.

 \
The probability that a non-catastrophic $(2,1,1)$ convolutional code is MDP, reverse MDP or complete MDP is $\frac{(1-t)(1-2t)}{1+t}$.

 \
The conditions on the generator matrix $G(z)$ to get an MDP, reverse MDP or complete MDP convolutional code imply that the two entries of $G(z)$ are of degree one and have a different zero. This means that the entries of $G(z)$ are coprime. Thus, each $(2,1,1)$ MDP convolutional code is non-catastrophic. Consequently, to obtain the conditional probability (under the condition that the code is non-catastrophic), one has just to divide the probability of the first theorem by the 