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Abstract A convolutional code C over Z p r ((D)) is a Z p r ((D)) -submodule of Z p r n ((D)) that admits a polynomial set of generators, where Z p r ((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. [ABSTRACT FROM AUTHOR]