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In this work we present a way to construct the so-called root diagram forone-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 getan algorithm to obtain a Gr\"obner basis for the submodule $\overline{C}$associated to $C$

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