# On Gr\"obner Basis for certain one-point AG codes

## TL;DR

This paper introduces a method to construct root diagrams for specific one-point algebraic geometry codes, enabling an algorithmic approach to compute Gr"obner bases for related modules, which aids in code analysis.

## Contribution

It presents a novel construction of root diagrams for certain algebraic geometry codes, facilitating the computation of Gr"obner bases for associated modules.

## Key findings

- Root diagrams can be constructed for codes from certain curves.
- An algorithm for Gr"obner basis computation is developed.
- The method simplifies analysis of one-point AG codes.

## Abstract

In this work we present a way to construct the so-called root diagram for one-point AG codes $C$ arising from certain types of curves $\mathcal{X}$ over $\mathbb{F}_q$ with plane model $f(y)=g(x)$. Using this root diagram we can get an algorithm to obtain a Gr\"obner basis for the submodule $\overline{C}$ associated to $C$