One- and Two-Point Codes over Kummer Extensions

Abstract

We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^m=f(x{)}^{\lambda }$ where $f(x)$ is a separable polynomial over ${\mathbb{F}}_q$. In addition, we compute the Weierstrass semigroup at two certain totally ramified places. We then apply our results to construct one- and two-point algebraic geometric codes with good parameters.

Some corrections were made. Final version to appear in the IEEE Transactions on Information Theory

Cited by in corpus (4)

• Weierstrass Semigroups from Kummer Extensions
• Multi-point Codes over Kummer Extensions
• Pure gaps on curves with many rational places
• Weierstrass Semigroup, Pure Gaps and Codes on Function Fields