Weierstrass semigroups and the order bound
Provides an accessible introduction to a specialized topic for researchers in algebraic geometry and coding theory.
This survey introduces Weierstrass semigroups in the context of Stöhr-Voloch theory and discusses the Feng-Rao bound for dual minimum distance of one-point algebraic geometry codes.
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. Stöhr and J.F. Voloch. Furthermore, we discuss an application of Stöhr-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.