On the completeness of plane cubic curves over finite fields

DOI10.1007/s10623-016-0215-6zbMath1365.14041OpenAlexW2407511624MaRDI QIDQ522201

Stefano Marcugini, Fernanda Pambianco, Daniele Bartoli

Publication date: 13 April 2017

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-016-0215-6

zbMATH Keywords

\((n,3)\)-arcnear MDS codesplane algebraic cubic

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Blocking sets, ovals, (k)-arcs (51E21) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52)

Related Items (5)

Plane curves giving rise to blocking sets over finite fields ⋮ On complete \(m\)-arcs ⋮ Algebraic constructions of complete \(m\)-arcs ⋮ On near-MDS codes and caps ⋮ On the completeness of plane cubic curves over finite fields

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the completeness of plane cubic curves over finite fields
• Nonsingular plane cubic curves over finite fields
• Simple constructions for elliptic cubic curves with specified small numbers of points
• The number of points on an elliptic cubic curve over a finite field
• Some results concerning \(\{(q+1)(n-1);\;n\}\)-arcs and \(\{(q+1)\;(n-1)+1;\;n\}\)-arcs in finite projective planes of order \(q\)
• The Magma algebra system. I: The user language
• On plane arcs contained in cubic curves
• On the extendibility of near-MDS elliptic codes
• On near-MDS codes
• Near-MDS codes over some small fields
• The non-existence of some NMDS codes and the extremal sizes of complete \((n,3)\)-arcs in \(\mathrm{PG}(2,16)\)
• Small complete caps from singular cubics. II
• Bounds on \((n,r)\)-arcs and their application to linear codes
• The complete (k, 3)-arcs of PG(2,q), q≤13
• Abelian varieties over finite fields
• Ovali ed altre curve nei piani di Galois di caratteristica due

This page was built for publication: On the completeness of plane cubic curves over finite fields