Multi-Point AG Codes on the GK Maximal Curves

TL;DR

This paper explores multi-point algebraic-geometric codes derived from the GK maximal curve, focusing on code construction using divisors invariant under the curve's automorphisms, resulting in codes with large symmetry groups.

Contribution

It introduces new families of algebraic-geometric codes based on the GK maximal curve with large automorphism groups, highlighting their construction and properties.

Findings

Constructed new code families with large automorphism groups

Demonstrated invariance of divisors under automorphisms

Enhanced understanding of algebraic-geometric codes on GK curves

Abstract

In this paper we investigate multi-point Algebraic-Geometric codes associated to the GK maximal curve, starting from a divisor which is invariant under a large automorphism group of the curve. We construct families of codes with large automorphism groups.