Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes

TL;DR

This paper extends a fast list decoding algorithm for Hermitian codes to a broader class of one-point algebraic geometry codes, enabling more efficient decoding under weaker assumptions.

Contribution

It generalizes Lee and O'Sullivan's list decoding algorithm to all one-point AG codes with weaker assumptions than previous methods.

Findings

Enables application of the fast decoding algorithm to a wider class of codes.

Reduces the assumptions needed for successful list decoding.

Improves decoding efficiency for algebraic geometry codes.

Abstract

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables us to apply the fast algorithm to compute a Gr\"obner basis of a module proposed by Lee and O'Sullivan, which was not possible in another generalization by Lax.