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

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 (J Pure Appl Algebra 220:1122–1132, 2016) as new examples of curves which cannot be covered by the Hermitian curve.