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

Abstract

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.

22 pages, to appear in "Finite Fields and their Applications"