On duals and parity-checks of convolutional codes over Zpr

A convolutional code C over Zpr((D)) is a Zpr((D))-submodule of Zprn((D)) that admits a polynomial set of generators, where Zpr((D)) stands for the ring of (semi-infinity) Laurent series. In this paper we study several structural properties of its dual C⊥. We use these results to provide a constructive algorithm to build an explicit generator matrix of C⊥. Moreover, we show that the transpose of such a matrix is a parity-check matrix (also called syndrome former) of C.