The performance of Rosenthal’s decoding algorithm is measured when it is applied to certain family of 1-dimensional MDS convolutional codes. It is shown that the performance of this algorithm depends on the algebraic structure of the convolutional code we are working with.

Convolutional Goppa codes (CGC) were defined in Appl. Algebra Eng. Comm. Comput., vol. 15, pp. 51-61, 2004 and IEEE Trans. Inf. Theory, vol. 52, 340-344, 2006. In this paper, we prove that every convolutional code is a CGC defined over a smooth curve over$ \BBF _{q}(z)$and we give an explicit construction of convolutional codes as CGC over the projective line$ \BBP _{ \BBF _{q}(z)}^{1}$. We characterize which convolutional codes are defined by a complete linear system over curves of genus 0, 1, and over hyperelliptic curves. We apply these results to provide detailed constructions of some linear block codes as Goppa codes.

In this correspondence, we define convolutional Goppa codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some maximum-distance separable (MDS) convolutional codes.