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

被引：1

作者：

Montanucci, M. ^{[1
]}

Tizziotti, G. ^{[2
]}

机构：

[1] Tech Univ Denmark, Copenhagen, Denmark

[2] Univ Fed Uberlandia, Uberlandia, MG, Brazil

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 03期

关键词：

AG codes; Maximal curves; Generalized Weierstrass semigroup; AG CODES; MINIMUM DISTANCE; GAPS; QUOTIENT; FAMILY;

D O I：

10.1007/s10623-022-01130-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we determine the generalized Weierstrass semigroup P5,), and consequently the Weierstrass semigroup H(P-infinity,, P-1..., P-m), at ni + 1 points on the curves and Y,,. 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.

引用

页码：831 / 851

页数：21

共 8 条

[1] 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
[2] Weierstrass semigroup at m+1 rational points inmaximal curves which cannot be covered by the Hermitian curve
Castellanos, Alonso Sepulveda
Bras-Amoros, Maria
DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (08) : 1595 - 1616
[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] Triples of rational points on the Hermitian curve and their Weierstrass semigroups
Matthews, Gretchen L.
Skabelund, Dane
Wills, Michael
JOURNAL OF PURE AND APPLIED ALGEBRA, 2021, 225 (08)
[5] On maximal curves which are not Galois subcovers of the Hermitian curve
Iwan Duursma
Kit-Ho Mak
Bulletin of the Brazilian Mathematical Society, New Series, 2012, 43 : 453 - 465
[6] On maximal curves which are not Galois subcovers of the Hermitian curve
Duursma, Iwan
Mak, Kit-Ho
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2012, 43 (03): : 453 - 465
[7] Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables
Tenorio, Wanderson
Tizziotti, Guilherme
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 57 : 230 - 248
[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

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