Weierstrass semigroups on the Skabelund maximal curve

Peter  Beelen; Leonardo Landi; Maria Montanucci

doi:10.1016/j.ffa.2021.101811

Weierstrass semigroups on the Skabelund maximal curve

Peter Beelen
, Leonardo Landi
, Maria Montanucci^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

In [14], D. Skabelund constructed a maximal curve over F_q⁴ 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 F_q⁴ -rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the F_q-rational points, one for the remaining F_q⁴ -rational points. For each of these two types its Apéry set is computed as well as a set of generators.

Original language	English
Article number	101811
Journal	Finite Fields and Their Applications
Volume	72
Number of pages	31
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2021.101811
Publication status	Published - 2021

Keywords

Finite field
Maximal curve
Suzuki curve
Weierstrass semigroup
Weierstrass points

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10.1016/j.ffa.2021.101811

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title = "Weierstrass semigroups on the Skabelund maximal curve",

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 Ap{\'e}ry set is computed as well as a set of generators.",

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author = "Peter Beelen and Leonardo Landi and Maria Montanucci",

year = "2021",

doi = "10.1016/j.ffa.2021.101811",

language = "English",

volume = "72",

journal = "Finite Fields and Their Applications",

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T1 - Weierstrass semigroups on the Skabelund maximal curve

AU - Beelen, Peter

AU - Landi, Leonardo

AU - Montanucci, Maria

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Finite field

KW - Maximal curve

KW - Suzuki curve

KW - Weierstrass semigroup

KW - Weierstrass points

U2 - 10.1016/j.ffa.2021.101811

DO - 10.1016/j.ffa.2021.101811

M3 - Journal article

SN - 1071-5797

VL - 72

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

M1 - 101811

ER -

Weierstrass semigroups on the Skabelund maximal curve

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Keywords

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