English

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 H(P,P1,,Pm)H(P_\infty,P_1,\ldots,P_m) 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}
}