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

Universidad Nacional del Litoral, Argentina   -   cabanagusti@gmail.com

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.

Joint work with María Chara (Universidad Nacional del Litoral, Argentina), Ricardo Podestá (Universidad Nacional de Córdoba, Argentina) and Ricardo Toledano (Universidad Nacional del Litoral, Argentina).

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