Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models

We present an algorithm to compute the Weierstrass semigroup at a point P together with functions for each value in the semigroup, provided P is the only branch at infinity of a singular plane model for the curve. As a byproduct, the method also provides us with a basis for the spaces L(mP) and the computation of the Feng?Rao distance for the corresponding array of geometric Goppa codes. A general computation of the Feng?Rao distance is also obtained. Everything can be applied to the decoding problem by using the majority scheme of Feng and Rao.

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