Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve

Abstract

We determine the Weierstrass semigroup $H(P_{\infty },P_1,\dots ,P_m)$ at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced by Tafazolian, Teherán-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.

References in corpus (1)

• Bounding the number of rational places using Weierstrass semigroups