Two-point AG codes from the Beelen-Montanucci maximal curve
Leonardo Landi, Lara Vicino
TL;DR
This paper explores two-point algebraic-geometry codes derived from the Beelen-Montanucci maximal curve, identifying codes with improved parameters by analyzing Weierstrass semigroups and minimum distance bounds.
Contribution
It introduces new two-point AG codes from the BM curve with better parameters than those from the GGS curve, based on semigroup analysis and distance bounds.
Findings
Discovery of two-point AG codes with improved parameters.
Lower bounds on minimum distance for these codes.
Comparison showing superiority over GGS-based codes.
Abstract
In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-G\"uneri-Stichtenoth (GGS) curve are discovered.
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