An extension of the order bound for AG codes

TL;DR

This paper extends the order bound for algebraic geometric codes, improving minimum distance estimates, and provides extensive numerical comparisons for codes on Suzuki curves.

Contribution

It introduces a significant extension of the order bound, enhancing previous bounds by Beelen and Duursma-Park, with comprehensive numerical analysis.

Findings

Extended the order bound for AG codes

Improved minimum distance bounds for two-point codes

Performed extensive numerical comparisons on Suzuki curve codes

Abstract

The most successful method to obtain lower bounds for the minimum distance of an algebraic geometric code is the order bound, which generalizes the Feng-Rao bound. We provide a significant extension of the bound that improves the order bounds by Beelen and by Duursma and Park. We include an exhaustive numerical comparison of the different bounds for 10168 two-point codes on the Suzuki curve of genus g=124 over the field of 32 elements. Keywords: algebraic geometric code, order bound, Suzuki curve.