Rational points on cubic surfaces and AG codes from the Norm-Trace curve

Abstract

In this paper we give a complete characterization of the intersections between the Norm-Trace curve over ${\mathbb{F}}_{q^3}$ and the curves of the form $y=a{x}^3+b{x}^2+cx+d$, generalizing a previous result by Bonini and Sala, providing more detailed information about the weight spectrum of one-point AG codes arising from such curve. We also derive, with explicit computations, some general bounds for the number of rational points on a cubic surface defined over ${\mathbb{F}}_q$.

References in corpus (1)

• On the Hermitian curve and its intersections with some conics