On the Parameters of Convolutional Codes with Cyclic Structure

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.