An improvement of the Feng-Rao bound for primary codes

TL;DR

This paper introduces an enhanced bound for the minimum distance of primary linear codes, especially effective for affine variety codes from generalized C_{ab} curves, and applicable to Hamming weights.

Contribution

It proposes a new bound that improves upon the Feng-Rao bound for primary codes and extends to generalized Hamming weights.

Findings

The new bound often significantly outperforms the Feng-Rao bound for affine variety codes.

The method applies broadly to minimum distance and Hamming weights.

Enhanced bounds lead to better code performance estimates.

Abstract

We present a new bound for the minimum distance of a general primary linear code. For affine variety codes defined from generalised C_{ab} curves the new bound often improves dramatically on the Feng-Rao bound for primary codes. The method does not only work for the minimum distance but can be applied to any generalised Hamming weight