On the weights of dual codes arising from the GK curve

TL;DR

This paper studies dual algebraic-geometric codes from the Giulietti-Korchmaros curve, focusing on their minimum distance, weight codewords, and generalized Hamming weights to understand their error-correcting capabilities.

Contribution

It provides explicit calculations of minimum distances, weight codewords, and generalized Hamming weights for codes from the GK curve, advancing understanding of their algebraic structure.

Findings

Determined the minimum distance of the codes.

Identified the structure of minimum weight codewords.

Analyzed the generalized Hamming weights of the codes.

Abstract

In this paper we investigate some dual algebraic-geometric codes associated with the Giulietti-Korchm\'aros maximal curve. We compute the minimum distance and the minimum weight codewords of such codes and we investigate the generalized hamming weights of such codes.