Minimum weight codewords in dual Algebraic-Geometric codes from the Giulietti-Korchm\'aros curve
Daniele Bartoli, Matteo Bonini
TL;DR
This paper studies the minimum weight codewords in dual algebraic-geometric codes derived from the Giulietti-Korchmárós curve by analyzing intersections with low-degree curves.
Contribution
It provides a detailed computation of the maximum intersections with lines, conics, and cubics to determine the number of minimum weight codewords.
Findings
Maximum intersection counts with lines, conics, and cubics are established.
Results help characterize the minimum weight codewords in the codes.
The approach advances understanding of algebraic-geometric code structures.
Abstract
In this paper we investigate the number of minimum weight codewords of some dual Algebraic-Geometric codes associated with the Giulietti-Korchm\'aros maximal curve, by computing the maximal number of intersections between the Giulietti-Korchm\'aros curve and lines, plane conics and plane cubics.
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