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

Matteo Bonini; Massimiliano Sala; Lara Vicino

doi:10.1007/s10231-022-01237-3

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

Matteo Bonini, Massimiliano Sala, Lara Vicino^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper, we derive general bounds for the number of rational points on a cubic surface defined over
, which constitute an extension of a result due to Weil. Exploiting these bounds, we are able to 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 and providing more detailed information about the weight spectrum of one-point AG codes arising from such curve.

Original language	English
Pages (from-to)	185–208
Number of pages	24
Journal	Annali di Matematica Pura ed Applicata
Volume	202
DOIs	https://doi.org/10.1007/s10231-022-01237-3
Publication status	Published - Feb-2023
Externally published	Yes

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title = "Rational points on cubic surfaces and AG codes from the Norm–Trace curve",

abstract = "In this paper, we derive general bounds for the number of rational points on a cubic surface defined over , which constitute an extension of a result due to Weil. Exploiting these bounds, we are able to 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 and providing more detailed information about the weight spectrum of one-point AG codes arising from such curve.",

author = "Matteo Bonini and Massimiliano Sala and Lara Vicino",

year = "2023",

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doi = "10.1007/s10231-022-01237-3",

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T1 - Rational points on cubic surfaces and AG codes from the Norm–Trace curve

AU - Bonini, Matteo

AU - Sala, Massimiliano

AU - Vicino, Lara

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N2 - In this paper, we derive general bounds for the number of rational points on a cubic surface defined over , which constitute an extension of a result due to Weil. Exploiting these bounds, we are able to 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 and providing more detailed information about the weight spectrum of one-point AG codes arising from such curve.

AB - In this paper, we derive general bounds for the number of rational points on a cubic surface defined over , which constitute an extension of a result due to Weil. Exploiting these bounds, we are able to 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 and providing more detailed information about the weight spectrum of one-point AG codes arising from such curve.

U2 - 10.1007/s10231-022-01237-3

DO - 10.1007/s10231-022-01237-3

M3 - Article

SN - 0373-3114

VL - 202

SP - 185

EP - 208

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

ER -

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

Abstract

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