## 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

#### Universidad Nacional del Litoral, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakbdbb787d0e2d2342c60a7a58611a4f18').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addybdbb787d0e2d2342c60a7a58611a4f18 = 'c&#97;b&#97;n&#97;g&#117;st&#105;' + '&#64;'; addybdbb787d0e2d2342c60a7a58611a4f18 = addybdbb787d0e2d2342c60a7a58611a4f18 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_textbdbb787d0e2d2342c60a7a58611a4f18 = 'c&#97;b&#97;n&#97;g&#117;st&#105;' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloakbdbb787d0e2d2342c60a7a58611a4f18').innerHTML += '<a ' + path + '\'' + prefix + ':' + addybdbb787d0e2d2342c60a7a58611a4f18 + '\'>'+addy_textbdbb787d0e2d2342c60a7a58611a4f18+'<\/a>';

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).