On the automorphism group of a family of maximal curves not covered by the Hermitian curve

Maria Montanucci; Guilherme Tizziotti; Giovanni Zini

doi:10.1016/j.ffa.2024.102498

On the automorphism group of a family of maximal curves not covered by the Hermitian curve

Maria Montanucci
, Guilherme Tizziotti
, Giovanni Zini

Universidade Federal de Uberlândia
University of Modena and Reggio Emilia

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

Abstract

In this paper we compute the automorphism group of the curves X_a,b,n,s and Y_n,s introduced in Tafazolian et al. [27] as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained.

Original language	English
Article number	102498
Journal	Finite Fields and Their Applications
Volume	99
Number of pages	27
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2024.102498
Publication status	Published - 2024

Keywords

Automorphism group
GK curve
Maximal curve

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10.1016/j.ffa.2024.102498

https://arxiv.org/pdf/2301.07423

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title = "On the automorphism group of a family of maximal curves not covered by the Hermitian curve",

abstract = "In this paper we compute the automorphism group of the curves Xa,b,n,s and Yn,s introduced in Tafazolian et al. [27] as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained.",

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T1 - On the automorphism group of a family of maximal curves not covered by the Hermitian curve

AU - Montanucci, Maria

AU - Tizziotti, Guilherme

AU - Zini, Giovanni

PY - 2024

Y1 - 2024

N2 - In this paper we compute the automorphism group of the curves Xa,b,n,s and Yn,s introduced in Tafazolian et al. [27] as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained.

AB - In this paper we compute the automorphism group of the curves Xa,b,n,s and Yn,s introduced in Tafazolian et al. [27] as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained.

KW - Automorphism group

KW - GK curve

KW - Maximal curve

U2 - 10.1016/j.ffa.2024.102498

DO - 10.1016/j.ffa.2024.102498

M3 - Journal article

SN - 1071-5797

VL - 99

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

M1 - 102498

ER -

On the automorphism group of a family of maximal curves not covered by the Hermitian curve

Abstract

Keywords

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