Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

TL;DR

This paper determines the generalized Weierstrass semigroup at multiple points on certain maximal curves that are not covered by Hermitian curves, expanding understanding of their algebraic structure.

Contribution

It explicitly computes the generalized Weierstrass semigroup at several points on new maximal curves not related to Hermitian curves.

Findings

Determined the semigroup structure for specific maximal curves.

Extended the class of curves with known Weierstrass semigroups.

Provided tools for algebraic geometry and coding theory applications.

Abstract

In this paper we determine the generalized Weierstrass semigroup $ \widehat{H}(P_{\infty}, P_1, \ldots , P_{m})$, and consequently the Weierstrass semigroup $H(P_{\infty}, P_1, \ldots , P_{m})$, at $m+1$ points on the curves $\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$. These curves has been introduced in Tafazolian et al. as new examples of curves which cannot be covered by the Hermitian curve.