Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve
Algebraic Geometry
2021-06-25 v1 Information Theory
math.IT
Abstract
We determine the Weierstrass semigroup at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced by Tafazolian, Teher\'an-Herrera, and Torres. Furthermore, we present some conditions to find pure gaps. We use this semigroup to obtain AG codes with better relative parameters than comparable one-point AG codes arising from these curves.
Keywords
Cite
@article{arxiv.2106.13159,
title = {Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve},
author = {Alonso Sepúlveda Castellanos and Maria Bras-Amorós},
journal= {arXiv preprint arXiv:2106.13159},
year = {2021}
}