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 and the curves of the form , 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 .
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}
}