Can I read Weierstrass Semigroup, Pure Gaps and Codes on Function Fields on EtoBox?

Weierstrass Semigroup, Pure Gaps and Codes on Function Fields by Castellanos, Alonso S.; Mendoza, Erik A. R.; Quoos, Luciane is a scholarly article available to read on EtoBox.

What is Weierstrass Semigroup, Pure Gaps and Codes on Function Fields about?

We determine the Weierstrass semigroup at one and two totally ramified places in a Kummer extension defined by the affine equation $y^{m}=\prod_{i=1}^{r} (x-\alpha_i)^{\lambda_i}$ over $K$, the algebraic closure of $\mathbb{F}_q$, where $\alpha_1, \dots, \alpha_r\in K$ are pairwise distinct elements, and $\gcd(m, \sum_{i=1}^{r}\lambda_i)=1$. For an arbitrary function field, from the knowledge of the minimal generating set of the Weierstrass semigroup at two rational places, the set of pure gaps is characterized. We apply these results to construct algebraic geometry codes over certain function fields with many rational places.

Author

Castellanos, Alonso S.; Mendoza, Erik A. R.; Quoos, Luciane

Published

2023

Language

EN