Two-point AG codes on the GK maximal curves
Alonso Sep\'ulveda, Guilherme Tizziotti
TL;DR
This paper computes the Weierstrass semigroup for pairs of points on GK-curves to construct two-point algebraic geometry codes with improved parameters, setting new records in coding tables.
Contribution
It introduces a method to determine the Weierstrass semigroup for pairs of points on GK-curves, enabling the construction of superior two-point AG codes.
Findings
Two-point AG codes outperform one-point codes on GK-curves.
New record parameters established in MinT's tables.
Method for semigroup determination enhances code construction.
Abstract
We determine de Weierstrass semigroup of a pair of certain rational points on the GK-curves. We use this semigroup to obtain two-point AG codes with better parameters than comparable one-point AG codes arising from these curves. These parameters are new records in the MinT's tables.
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Taxonomy
TopicsCoding theory and cryptography · Cancer Mechanisms and Therapy