# Two-Point Codes for the Generalized GK curve

## TL;DR

This paper enhances lower bounds for the minimum distance of two-point algebraic geometry codes from generalized Giulietti-Korchmaros curves, offering improved bounds and an efficient algorithm for their computation.

## Contribution

It introduces new bounds for two-point AG codes on GGK curves, surpassing previous results and providing a practical algorithm for their calculation.

## Key findings

- Improved minimum distance bounds for GGK-based two-point codes
- Complete coverage and enhancement of previous bounds by Castellanos and Tizziotti
- New entries in MinT minimum distance tables

## Abstract

We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti-Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.