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 (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.