Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models
Algebraic Geometry
2025-10-20 v1 Information Theory
Numerical Analysis
math.IT
Numerical Analysis
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.
Cite
@article{arxiv.math/9910155,
title = {Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models},
author = {A. Campillo and J. I. Farran},
journal= {arXiv preprint arXiv:math/9910155},
year = {2025}
}
Comments
22 pages, to appear in "Finite Fields and their Applications"