Transitive \(\mathrm{PSL}(2,7)\)-invariant 42-arcs in 3-dimensional projective spaces

DOI10.1007/s10623-012-9778-zzbMath1321.51010OpenAlexW2093969646MaRDI QIDQ2248654

Angelo Sonnino

Publication date: 27 June 2014

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

Full work available at URL: https://doi.org/10.1007/s10623-012-9778-z

zbMATH Keywords

finite projective space\(k\)-arc\(\mathrm{PSL}(2,7)\)

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Combinatorial structures in finite projective spaces (51E20)

Related Items (4)

Upper bounds on the length function for covering codes with covering radius \(R\) and codimension \(tR+1\) ⋮ On linear codes admitting large automorphism groups ⋮ Transitive \(\mathrm{PSL}(2,11)\)-invariant \(k\)-arcs in \(\mathrm{PG}(4,q)\) ⋮ On the existence of PD-sets: algorithms arising from automorphism groups of codes

Uses Software

• GAP

Cites Work

• 42-arcs in \(\mathrm{PG}(2, q)\) left invariant by \(\mathrm{PSL}(2, 7)\)
• Projective \(k\)-arcs and 2-level secret-sharing schemes
• Linear nonbinary covering codes and saturating sets in projective spaces
• Three-level secret sharing schemes from the twisted cubic
• Linear collineation groups preserving an arc in a Möbius plane
• Large \(k\)-arcs in inversive planes of odd order
• Transitive \(A_6\)-invariant \(k\)-arcs in \(\mathrm{PG}(2,q)\)
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