On complete \((N,d)\)-arcs derived from plane curves

DOI10.1016/j.ffa.2008.08.003zbMath1179.14029OpenAlexW2091038033MaRDI QIDQ2517817

Herivelto Borges

Publication date: 9 January 2009

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2008.08.003

zbMATH Keywords

arcsFermat curvescomplete \((k, n)\)-arcscomplete \((N, d)\)-arcs

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Finite ground fields in algebraic geometry (14G15) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (7)

Plane curves giving rise to blocking sets over finite fields ⋮ Algebraic approach to the completeness problem for \((k,n)\)-arcs in planes over finite fields ⋮ Sharp Bertini Theorem for Plane Curves over Finite Fields ⋮ Frobenius nonclassicality of Fermat curves with respect to cubics ⋮ The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines ⋮ Frobenius nonclassical components of curves with separated variables ⋮ On multi-Frobenius non-classical plane curves

Cites Work

• On \((k,n)\)-arcs
• Affine blocking sets, three-dimensional codes and the Griesmer bound
• Frobenius non classical curves
• Fermat curves over finite fields
• On complete arcs arising from plane curves
• On the number of rational points on some families of Fermat curves over finite fields
• Bounds on \((n,r)\)-arcs and their application to linear codes
• Constructions of plane curves with many points
• Weierstrass Points and Curves Over Finite Fields
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