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arXiv · 2605.01348

Weierstrass semigroups and the order bound

Alix Barraud·Yağmur Çakıroğlu·Bianca Gouthier·Gretchen L. Matthews·Lara Vicino
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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.

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Alix Barraud, Yağmur Çakıroğlu, Bianca Gouthier, Gretchen L. Matthews, Lara Vicino. 2026-05-02. Weierstrass semigroups and the order bound. https://arxiv.org/abs/2605.01348

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