Weierstrass semigroups and the order bound
Algebraic Geometry
2026-05-06 v1 Information Theory
math.IT
Abstract
The aim of this survey is to provide the reader with an essential and accessible introduction to the theory of Weierstrass semigroups, in the context of the theory developed by K.-O. St\"ohr and J.F. Voloch. Furthermore, we discuss an application of St\"ohr-Voloch theory in coding theory, namely the Feng-Rao bound (also known as the order bound) for the dual minimum distance of one-point algebraic geometry codes from a curve, which relies on the knowledge of certain Weierstrass semigroups of the curve.
Cite
@article{arxiv.2605.01348,
title = {Weierstrass semigroups and the order bound},
author = {Alix Barraud and Yağmur Çakıroğlu and Bianca Gouthier and Gretchen L. Matthews and Lara Vicino},
journal= {arXiv preprint arXiv:2605.01348},
year = {2026}
}