English

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

Algebraic Geometry 2022-07-05 v1 Information Theory math.IT

Abstract

In this paper we give a complete characterization of the intersections between the Norm-Trace curve over Fq3\mathbb{F}_{q^3} and the curves of the form y=ax3+bx2+cx+dy=ax^3+bx^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 Fq\mathbb{F}_{q}.

Keywords

Cite

@article{arxiv.2102.05478,
  title  = {Rational points on cubic surfaces and AG codes from the Norm-Trace curve},
  author = {Matteo Bonini and Massimiliano Sala and Lara Vicino},
  journal= {arXiv preprint arXiv:2102.05478},
  year   = {2022}
}
R2 v1 2026-06-23T23:01:59.756Z