Further improvements on the Feng-Rao bound for dual codes

TL;DR

This paper advances the Feng-Rao bound for dual codes by extending it to generalized Hamming weights and highlights the benefits of using one-way well-behaving pairs over other pair types.

Contribution

It introduces a further improvement to the Feng-Rao bound, extending its applicability to generalized Hamming weights and emphasizing the effectiveness of one-way well-behaving pairs.

Findings

The improved bound applies to generalized Hamming weights.

Using one-way well-behaving pairs yields better bounds.

The approach enhances the estimation of minimum distances in dual codes.

Abstract

Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly well-behaving or well-behaving pairs.