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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  that only certain combinations of the algebraic parameters (field size, length, dimension, and Forney indices) can occur for such 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 completedoi:10.1142/s0219498806001570 fatcat:szj6gnbldrd5jovjxtkdpeo554