Two-point AG codes from one of the Skabelund maximal curves

TL;DR

This paper studies two-point algebraic geometry codes derived from the Skabelund maximal curve, focusing on estimating their minimum distance using Weierstrass semigroups and the generalized order bound.

Contribution

It introduces a method to estimate the minimum distance of two-point AG codes from the Skabelund maximal curve by analyzing Weierstrass semigroups and applying the generalized order bound.

Findings

Determined specific two-point Weierstrass semigroups of the Skabelund maximal curve.

Estimated minimum distances of the associated two-point AG codes.

Applied the generalized order bound to improve code parameter bounds.

Abstract

In this paper, we investigate two-point Algebraic Geometry codes associated to the Skabelund maximal curve constructed as a cyclic cover of the Suzuki curve. In order to estimate the minimum distance of such codes, we make use of the generalized order bound introduced by P. Beelen and determine certain two-point Weierstrass semigroups of the curve.