Weierstrass semigroups and the order bound
Alix Barraud, Ya\u{g}mur \c{C}ak{\i}ro\u{g}lu, Bianca Gouthier, Gretchen L. Matthews, Lara Vicino
TL;DR
This survey introduces Weierstrass semigroups and explores their application in coding theory, specifically in improving bounds for algebraic geometry codes using St"ohr-Voloch theory.
Contribution
It provides an accessible overview of Weierstrass semigroups and discusses their role in applying the Feng-Rao (order) bound in coding theory.
Findings
Explains the connection between Weierstrass semigroups and the Feng-Rao bound.
Highlights the importance of Weierstrass semigroups in algebraic geometry codes.
Discusses the application of St"ohr-Voloch theory in coding bounds.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.