A generalization of the Giulietti–Korchmáros maximal curve-Reference-Cited by-同舟云学术

A generalization of the Giulietti–Korchmáros maximal curve

Published:2010-04-12 Issue:3 Volume:10 Page:427-434
ISSN:1615-7168
Container-title:advg
language:en
Short-container-title:

Author:

Garcia Arnaldo¹,Güneri Cem²,Stichtenoth Henning²

Affiliation:

1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. Email:

2. Sabancı University, FENS, 34956 Istanbul, Turkey. Email:

Abstract

Abstract We introduce a family of algebraic curves over 𝔽 q 2n (for an odd n) and show that they are maximal. When n = 3, our curve coincides with the 𝔽 q 6 -maximal curve that has been found by Giulietti and Korchmáros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to be covered by the Hermitian curve.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom.2010.020/pdf

Reference7 articles.

1. Further examples of maximal curves

2. On a characterization of certain maximal curves

3. On maximal curves in characteristic two

4. On Maximal Curves

Cited by 52 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the automorphism group of a family of maximal curves not covered by the Hermitian curve;Finite Fields and Their Applications;2024-10

2. Two-Point AG Codes From One of the Skabelund Maximal Curves;IEEE Transactions on Information Theory;2024-07

3. Lifting iso-dual algebraic geometry codes;Designs, Codes and Cryptography;2024-05-07

4. New sextics of genus 6 and 10 attaining the Serre bound;Advances in Geometry;2024-01-01

5. On the number of rational points on Artin-Schreier hypersurfaces;Finite Fields and Their Applications;2023-09