In this paper we analyze the intersection between the norm-trace curve over ${\mathbb{F}}_{q^3}$ and the curves of the form $y=a{x}^3+b{x}^2+cx+d$, giving a complete characterization of the intersection between the curve and the parabolas (a=0), 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 arising from the curve.

中文翻译：

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范数曲线和一些低度曲线之间的交点

在本文中，我们分析了规范曲线与曲线之间的交点。 ${\mathbb{F}}_{q^3}$ 和形式的曲线 $ÿ=\mathrm{一种}{X}^3+b{X}^2+CX+d$，可以完全表征曲线和抛物线之间的交点（a = 0），以及其他情况下的清晰边界。该信息用于确定由曲线产生的一些单点AG代码的权重分布。