  In this paper convolutional codes with cyclic structure will be investigated.
These codes can be understood as left principal ideals in a suitable
skew-polynomial ring. It has been shown in [3] that only certain combinations
of the parameters (field size, length, dimension, and Forney indices) can occur
for cyclic codes. We will investigate whether all these combinations can indeed
be realized by a suitable cyclic code and, if so, how to construct such a code.
A complete characterization and construction will be given for minimal cyclic
codes. It is derived from a detailed investigation of the units in the
skew-polynomial ring.
