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arXiv · 2102.05478

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

Matteo Bonini·Massimiliano Sala·Lara Vicino
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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 $y=ax^3+bx^2+cx+d$, 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 $\mathbb{F}_{q}$.

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Matteo Bonini, Massimiliano Sala, Lara Vicino. 2021-02-10. Rational points on cubic surfaces and AG codes from the Norm-Trace curve. https://doi.org/10.1007/s10231-022-01237-3

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