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Algebraic-geometric techniques to construct linear codes can be applied to construct convolutional codes, using algebraic curves over function fields. In this way we construct convolutional Goppa codes and provide a systematic way for constructing convolutional codes with prescribed properties. We study convolutional Goppa codes defined by the projective line and elliptic curves in detail.

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We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes ([1, 14]). Using this general construction we can give several examples of Maximum Distance Separable (MDS) Convolutional Codes.

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