Weierstrass semigroups on the Skabelund maximal curve

Peter Beelen, Leonardo Landi, Maria Montanucci*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In [14], D. Skabelund constructed a maximal curve over Fq4 as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point P of the Skabelund curve. We show that its Weierstrass points are precisely the Fq4 -rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the Fq-rational points, one for the remaining Fq4 -rational points. For each of these two types its Apéry set is computed as well as a set of generators.
Original languageEnglish
Article number101811
JournalFinite fields and their applications
Volume72
Number of pages31
ISSN1071-5797
DOIs
Publication statusPublished - 2021

Keywords

  • Finite field
  • Maximal curve
  • Suzuki curve
  • Weierstrass semigroup
  • Weierstrass points

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