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Mathematics > Combinatorics

arXiv:1812.08590 (math)
[Submitted on 20 Dec 2018 (v1), last revised 6 Mar 2020 (this version, v2)]

Title:Intersections between the norm-trace curve and some low degree curves

Authors:Matteo Bonini, Massimiliano Sala
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Abstract:In this paper we analyze the intersection between the norm-trace curve over $\mathbb{F}_{q^3}$ and the curves of the form $y=ax^3+bx^2+cx+d$, giving a complete characterization of the intersection between the curve and the parabolas, as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes constructed on the curve.
Subjects: Combinatorics (math.CO); Information Theory (cs.IT); Algebraic Geometry (math.AG)
MSC classes: 14G50 - 11T71 - 94B27
Cite as: arXiv:1812.08590 [math.CO]
  (or arXiv:1812.08590v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1812.08590

Submission history

From: Matteo Bonini [view email]
[v1] Thu, 20 Dec 2018 14:21:59 UTC (152 KB)
[v2] Fri, 6 Mar 2020 15:04:21 UTC (153 KB)
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