Automorphism groups of generalized Reed-Solomon codes

TL;DR

This paper re-examines the automorphism groups of algebraic geometry codes from the projective line, using algebraic geometry methods to classify possible groups and provide explicit descriptions, including examples with large automorphism groups.

Contribution

It introduces a new algebraic geometry approach to classify automorphism groups of AG codes from the projective line, expanding previous combinatorial results.

Findings

Classified finite groups as automorphism groups of AG codes

Provided explicit descriptions of group actions on codes

Constructed examples with large automorphism groups like PSL(2,q)

Abstract

We look at AG codes associated to the projective line, re-examining the problem of determining their automorphism groups (originally investigated by Duer in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We (re)classify those finite groups that can arise as the automorphism group of an AG code for the projective line and give an explicit description of how these groups appear. We also give examples of generalized Reed-Solomon codes with large automorphism groups G, such as G=PSL(2,q), and explicitly describe their G-module structure.