Computing the Automorphism Groups of Hyperelliptic Function Fields

2003/05/20 by Norbert Goeb, Goeb, Norbert
Computer Science · Mathematics · #11R58 #11Y99 #14H05 #14Q99 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R58 #msc:11Y99 #msc:14H05 #msc:14Q99

paper · pdf · doi:10.48550/arxiv.math/0305284

16 pages, to be presented at MEGA 2003 (see http://www.mathematik.uni-kl.de/~mega2003)

arxiv created 2003/05/20 · openalex publication_date 2003/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field (genus>1) over a given ground field of characteristic >2 as well as over its algebraic extensions.

Related

• Algorithmic study of superspecial hyperelliptic curves over finite fields
• The 2-ranks of Hyperelliptic Curves with Extra Automorphisms
• Generators in the field of hyperelliptic functions
• The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes
• Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields