## View abstract

### Session S26 - Finite fields and applications

Thursday, July 15, 11:30 ~ 11:50 UTC-3

## On the classification of some Rational Cyclic AG Codes.

### Gustavo Andrés Cabaña

Let $F$ be the rational function field $\mathbb{F}_{q}(x)$ and $A=\mathrm{Aut}_{\mathbb{F}_{q}}(F)$. Consider $\sigma \in A$ and $P_{1},P_{2},\ldots ,P_{n},Q$ rational places of $F$ such that $\sigma(P_{i})=P_{i+1 \; \mathrm{mod} \; n}$ and $\sigma(Q)=Q$.
Let $D,G$ be divisors of $F$ given by $D=P_{1}+P_{2}+ \cdots + P_{n}$ and $G=rQ$ for some integer $r>0$.
We study AG codes $\mathcal{C_{L}}(D,G)$, which are cyclic AG codes, and we prove that, up to monomial equivalence, there is only one code in this family of a fixed length and dimension.