The genus of maximal function fields over finite fields
type: Item
instance of: scholarly article
title: The genus of maximal function fields over finite fields
zbMATH Open document ID: 0826.11054
DOI: 10.1007/BF02567990
author: Henning Stichtenoth
author: Chaoping Xing
published in: Manuscripta Mathematica
publication date: 1995-03-13T00:00:00Z
full work available at URL: https://eudml.org/doc/156050
review text: It is proved that if there exists a maximal function field of genus \(g\) over the finite field with \(q^2\) elements, then \(g\leq (q-1)^2/4\) or \(g= qr/2\) with \((q-1)/2\leq r\leq q-1\). The authors conjecture that in the second case \(r= (q-1)\). This conjecture has been proved in the affirmative by Fuhrmann and Torres.
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 733203
zbMATH Keywords: maximal curves over finite fields
zbMATH Keywords: maximal function field
reviewed by: Ruud Pellikaan
MaRDI profile type: Publication
cites work: Q3941473
cites work: On a decoding algorithm for codes on maximal curves
cites work: Algebraic function fields and codes
description: scientific article; zbMATH DE number 733203