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An important class of codes widely used in applications is the class ofconvolutional codes. Most of the literature of convolutional codes is devotedto con- volutional codes over finite fields. The extension of the concept ofconvolutional codes from finite fields to finite rings have attracted muchattention in recent years due to fact that they are the most appropriate codesfor phase modulation. However convolutional codes over finite rings are moreinvolved and not fully understood. Many results and features that arewell-known for convolutional codes over finite fields have not been fullyinvestigated in the context of finite rings. In this paper we focus in one ofthese unexplored areas, namely, we investigate the dual codes of convolutionalcodes over finite rings. In particular we study the p-dimension of the dualcode of a convolutional code over a finite ring. This contribution can beconsidered a generalization and an extension, to the rings case, of the workdone by Forney and McEliece on the dimension of the dual code of aconvolutional code over a finite field.

The dual of convolutional codes over $\mathbb{Z}_{p^r}$