  It is known that maximum distance separable and maximum distance profile
convolutional codes exist over large enough finite fields of any characteristic
for all parameters $(n,k,\delta)$. It has been conjectured that the same is
true for convolutional codes that are strongly maximum distance separable.
Using methods from linear systems theory, we resolve this conjecture by showing
that, over a large enough finite field of any characteristic, codes which are
simultaneously maximum distance profile and strongly maximum distance separable
exist for all parameters $(n,k,\delta)$.
