The algebraic geometric tools used by Goppa to construct block codes with good properties have been also used successfully in the setting of convolutional codes. We present here this construction carried out over elliptic curves, yielding a variety of codes which are optimal with respect to different bounds. We provide a number of examples for different values of their parameters, including some explicit strongly MDS convolutional codes. We also introduce some conditions for certain codes of this class to be MDS.
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