A note on certain maximal hyperelliptic curves
type: Item
instance of: scholarly article
title: A note on certain maximal hyperelliptic curves
zbMATH Open document ID: 1273.11100
author: Saeed Tafazolian
published in: Finite Fields and their Applications
publication date: 2012-10-11T00:00:00Z
review text: In this paper, the author gives necessary and sufficient conditions for a hyperelliptic curve of the form \(y^2=x^m+x\) to be maximal. More precisely, he proves that the curve \(y^2=x^{2g+1}+x\) is maximal over \(\mathbb{F}_{q^2}\) if and only if \(q\equiv -1\) or \(2g+1\pmod{4g}\), and the curve \(y^2=x^{2g+2}+x\) is maximal over the same field if and only if \(2g+1\) divides \(q+1\).
reviewed by: Kit Ho Mak
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 6092707
zbMATH Keywords: finite fields
zbMATH Keywords: maximal curves
zbMATH Keywords: hyperelliptic curves
MaRDI profile type: Publication
full work available at URL: j.ffa.2012.07.002
OpenAlex ID: W1993756116
cites work: A note on superspecial and maximal curves
cites work: Maximal hyperelliptic curves of genus three
cites work: A family of hyperelliptic function fields with Hasse-Witt-invariant zero
cites work: Algebraic Function Fields and Codes
cites work: A family of maximal hyperelliptic curves
DOI: 10.1016/J.FFA.2012.07.002
description: scientific article; zbMATH DE number 6092707