On saturating sets in projective spaces.

DOI10.1016/S0097-3165(03)00052-9zbMath1036.51006OpenAlexW2023820155MaRDI QIDQ1399903

Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco

Publication date: 30 July 2003

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0097-3165(03)00052-9

zbMATH Keywords

projective geometrysaturating setsCovering codes

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Linear codes and caps in Galois spaces (51E22) Combinatorial structures in finite projective spaces (51E20)

Related Items (12)

Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search ⋮ Small Complete Caps from Singular Cubics ⋮ Small complete caps in Galois affine spaces ⋮ Grassmannians of codes ⋮ Saturating systems and the rank-metric covering radius ⋮ Saturating linear sets of minimal rank ⋮ Saturating sets in projective planes and hypergraph covers ⋮ On the minimum size of complete arcs and minimal saturating sets in projective planes ⋮ Minimal 1-saturating sets and complete caps in binary projective spaces. ⋮ New bounds for linear codes of covering radii 2 and 3 ⋮ New covering codes of radius \(R\), codimension \(tr\) and \(tr+\frac{R}{2}\), and saturating sets in projective spaces ⋮ Upper bounds on the smallest size of a complete arc in \(\mathrm{PG}(2, {q})\) under a certain probabilistic conjecture

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some optimal codes from algebraic geometry and their covering radii
• Saturated configurations of points in projective Galois spaces
• On the spectrum of the values \(k\) for which a complete \(k\)-cap in \(PG(n,q)\) exists
• The packing problem in statistics, coding theory and finite projective spaces
• On saturating sets in small projective geometries
• On some 10-arcs for deriving the minimum order for complete arcs in small projective planes
• Small minimal blocking sets and complete \(k\)-arcs in PG\((2,p^3)\)
• Computer search for small complete caps
• Small complete caps in spaces of even characteristic
• Computer search in projective planes for the sizes of complete arcs
• Linear codes with covering radius R=2, 3 and codimension tR
• Constructions and families of nonbinary linear codes with covering radius 2
• Constructions and families of covering codes and saturated sets of points in projective geometry

This page was built for publication: On saturating sets in projective spaces.