On Gröbner Basis for certain 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 Gröbner basis for the submodule $\overline{C}$ associated to $C$

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