1999/10/28 by Antonio Campillo, Campillo, A., José Ignacio Farrán +1
Computer Science · #14Q05 (Primary) 11T71 (Secondary) #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Numerical Analysis (math.NA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/9910155
openalex publication_date 1999/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.