41 is the largest size of a cap in \(PG(4, 4)\)

DOI10.1023/A:1008389013117zbMath0935.51008OpenAlexW1929918490MaRDI QIDQ1299910

Yves Edel, Juergen Bierbrauer

Publication date: 25 April 2000

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

Full work available at URL: https://doi.org/10.1023/a:1008389013117

zbMATH Keywords

capfinite geometry

Mathematics Subject Classification ID

Linear codes and caps in Galois spaces (51E22) Combinatorial aspects of finite geometries (05B25)

Related Items (26)

Construction of quantum caps in projective space \(\mathrm{PG}(r,4)\) and quantum codes of distance 4 ⋮ New Quantum Caps in PG(4, 4) ⋮ On the Structure of Semiovals of Small Size ⋮ Unnamed Item ⋮ On \(k\)-caps in \(\mathrm{PG}(n, q)\), with \(q\) even and \(n \geq 4\) ⋮ The geometric approach to the existence of some quaternary Griesmer codes ⋮ On \(k\)-caps in \(\mathrm{PG}(n, q)\), with \(q\) even and \(n \geq 3\) ⋮ On the minimum size of complete arcs and minimal saturating sets in projective planes ⋮ Conics and caps ⋮ On complete caps in the projective geometries over \(\mathbb F_3\) ⋮ Large caps in projective space \(\mathrm{PG}(r, 4)\) ⋮ Completeness of the 95256-cap in \(\mathrm{PG}(12, 4)\) ⋮ The non-existence of some NMDS codes and the extremal sizes of complete \((n,3)\)-arcs in \(\mathrm{PG}(2,16)\) ⋮ The structure of quaternary quantum caps ⋮ Caps on classical varieties and their projections ⋮ Quantum codes from caps ⋮ Construction of caps by means of caps in complementary subspaces ⋮ Open problems in finite projective spaces ⋮ Maximal caps in \(\mathrm{AG}(6,3)\). ⋮ Sequences in abelian groups \(G\) of odd order without zero-sum subsequences of length \(\exp(G)\) ⋮ Caps in the projective geometry PG\((n,4)\) ⋮ New bounds for \(n_{4}(k,d)\) and classification of some optimal codes over GF(4) ⋮ On sizes of complete caps in projective spaces \(\mathrm{PG}(n, q)\) and arcs in planes \(\mathrm{PG}(2, q)\) ⋮ On the largest caps contained in the Klein quadric of \(PG(5,q)\), \(q\) odd ⋮ A family of caps in projective 4-space in odd characteristic ⋮ The classification of the largest caps in AG(5, 3)

This page was built for publication: 41 is the largest size of a cap in \(PG(4, 4)\)