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

被引：0

作者：

Montanucci, Maria ^{[1
]}

Tizziotti, Guilherme ^{[2
]}

Zini, Giovanni ^{[3
]}

机构：

[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, Kongens Lyngby 2800, Denmark

[2] Univ Fed Uberlandia, Fac Matemat, Uberlandia, Brazil

[3] Univ Modena & Reggio Emilia, Dept Phys Informat & Math, I-41125 Modena, Italy

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2024年 / 99卷

关键词：

Maximal curve; GK curve; Automorphism group; POINT AG CODES; FUNCTION-FIELDS; NUMBER;

D O I：

10.1016/j.ffa.2024.102498

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, anew characterization of the GK curve, as a member of this family, is obtained. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：27

共 50 条

[1] Curves covered by the Hermitian curve
Giulietti, M.
Hirschfeld, J. W. P.
Korchmaros, G.
Torres, F.
FINITE FIELDS AND THEIR APPLICATIONS, 2006, 12 (04) : 539 - 564
[2] On curves covered by the Hermitian curve
Cossidente, A
Korchmáros, G
Torres, F
JOURNAL OF ALGEBRA, 1999, 216 (01) : 56 - 76
[3] Further examples of maximal curves which cannot be covered by the Hermitian curve
Tafazolian, Saeed
Teheran-Herrera, Arnoldo
Torres, Fernando
JOURNAL OF PURE AND APPLIED ALGEBRA, 2016, 220 (03) : 1122 - 1132
[4] On maximal curves that are not quotients of the Hermitian curve
Giulietti, Massimo
Montanucci, Maria
Zini, Giovanni
FINITE FIELDS AND THEIR APPLICATIONS, 2016, 41 : 72 - 88
[5] The automorphism groups of a family of maximal curves
Guralnick, Robert
Malmskog, Beth
Pries, Rachel
JOURNAL OF ALGEBRA, 2012, 361 : 92 - 106
[6] Curves of large genus covered by the Hermitian curve
Cossidente, A
Korchmáros, G
Torres, F
COMMUNICATIONS IN ALGEBRA, 2000, 28 (10) : 4707 - 4728
[7] Mumford curves with maximal automorphism group
Cornelissen, G
Kato, F
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (07) : 1937 - 1941
[8] Fp2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
Bartoli, Daniele
Montanucci, Maria
Torres, Fernando
ADVANCES IN GEOMETRY, 2021, 21 (03) : 325 - 336
[9] Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve
Montanucci, M.
Tizziotti, G.
DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (03) : 831 - 851
[10] Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve
M. Montanucci
G. Tizziotti
Designs, Codes and Cryptography, 2023, 91 : 831 - 851

← 1 2 3 4 5 →