Details

Autor(en) / Beteiligte

• Bonini, Matteo
• Sala, Massimiliano
• Vicino, Lara

Titel

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

Ist Teil von

• Annali di matematica pura ed applicata, 2023-02, Vol.202 (1), p.185-208

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we derive general bounds for the number of rational points on a cubic surface defined over F q , 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 F q 3 and the curves of the form y = a x 3 + b x 2 + c x + d , 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.