Intersections between the normtrace curve and some low degree curves
Abstract
In this paper we analyze the intersection between the normtrace 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 onepoint AG codes constructed on the curve.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.08590
 Bibcode:
 2018arXiv181208590B
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Information Theory;
 Mathematics  Algebraic Geometry;
 14G50  11T71  94B27