The maximum size of a partial 3-spread in a finite vector space over \(\mathrm{GF}(2)\)

DOI10.1007/s10623-009-9311-1zbMath1200.51008OpenAlexW2045753079MaRDI QIDQ849358

Saad I. El-Zanati, Heather Jordon, Papa Amar Sissokho, Lawrence E. Spence, George F. Seelinger

Publication date: 25 February 2010

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

Full work available at URL: https://doi.org/10.1007/s10623-009-9311-1

zbMATH Keywords

spreadsorthogonal arrayspartial spreads\((s,k,\lambda)\)-nets

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Orthogonal arrays, Latin squares, Room squares (05B15) Finite partial geometries (general), nets, partial spreads (51E14) Combinatorial aspects of packing and covering (05B40)

Related Items (19)

Multicomponent codes with maximum code distance ⋮ A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS ⋮ Partial spreads in random network coding ⋮ Construction of subspace codes through linkage ⋮ The maximum size of a partial spread in a finite projective space ⋮ Improved upper bounds for partial spreads ⋮ Vector space partitions of GF(2)^8 ⋮ Galois geometries and coding theory ⋮ Extremal sizes of subspace partitions ⋮ Gaussian partitions ⋮ Classification of large partial plane spreads in \(\mathrm{PG}(6,2)\) and related combinatorial objects ⋮ New Lower Bounds for Binary Constant-Dimension Subspace Codes ⋮ The maximum size of a partial spread. II: Upper bounds ⋮ Partitions of finite vector spaces over \(\mathrm{GF}(2)\) into subspaces of dimensions 2 and \(s\) ⋮ The minimum size of a finite subspace partition ⋮ Partitions of the 8-dimensional vector space over GF(2) ⋮ Optimal Binary Linear Locally Repairable Codes with Disjoint Repair Groups ⋮ Equidistant codes in the Grassmannian ⋮ Cyclic orbit codes and stabilizer subfields

Cites Work

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• The maximum size of a partial spread in \(H(5,q^{2})\) is \(q^{3}+1\)
• On vector space partitions and uniformly resolvable designs
• On partitions of finite vector spaces of low dimension over \(\text{GF}(2)\)
• Partitions of finite Abelian groups
• Partial t-spreads and group constructible \((s,r,\mu)\)-nets
• Partitions of a vector space
• Partitions of finite vector spaces: an application of the Frobenius number in geometry
• A note on maximal partial spreads with deficiency \(q+1\), \(q\) even
• On maximal partial spreads in \(PG\)(\(n\), \(q\))
• On a particular class of minihypers and its applications. I: The result for general \(q\)
• On the spectrum of the sizes of maximal partial line spreads in \(\mathrm{PG}(2n,q)\), \(n \geq 3\)
• A General Class of Maximal Codes ror Computer Applications
• A maximal partial spread of size 45 in \(PG(3,7)\)
• Maximal partial spreads and the modular \(n\)-queen problem. III

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