A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS

DOI10.1142/S1793830912500012zbMath1255.51004arXiv1103.1031OpenAlexW2963376664MaRDI QIDQ2905300

Olof Heden

Publication date: 27 August 2012

Published in: Discrete Mathematics, Algorithms and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.1031

zbMATH Keywords

projective planemaximal partial spreadperfect codevector space partition\(t\)-spread

Mathematics Subject Classification ID

Steiner systems in finite geometry (51E10) Spreads and packing problems in finite geometry (51E23) Finite partial geometries (general), nets, partial spreads (51E14)

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Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces ⋮ The maximum size of a partial spread in a finite projective space ⋮ The supertail of a subspace partition ⋮ Vector space partitions of GF(2)^8 ⋮ Unnamed Item ⋮ Weighted external difference families and R-optimal AMD codes ⋮ Classification of large partial plane spreads in \(\mathrm{PG}(6,2)\) and related combinatorial objects ⋮ Subspace partitions of \(\mathbb{F}_q^n\) containing direct sums ⋮ The structure of the minimum size supertail of a subspace partition ⋮ The maximum size of a partial spread. II: Upper bounds ⋮ Characterising bimodal collections of sets in finite groups ⋮ Generalized vector space partitions ⋮ The complete characterization of the minimum size supertail in a subspace partition

Cites Work

• Some necessary conditions for vector space partitions
• Maximal partial spreads and the modular \(n\)-queen problem
• Partitionen endlicher Gruppen
• The maximum size of a partial 3-spread in a finite vector space over \(\mathrm{GF}(2)\)
• Necessary and sufficient conditions for the existence of a class of partitions of a finite vector space
• On partitions of finite vector spaces of low dimension over \(\text{GF}(2)\)
• The Frobenius number and partitions of a finite vector space
• Partitions of finite Abelian groups
• Partitions of a vector space
• Partial spreads, packings and Hermitian manifolds in \(PG(3,q)\)
• Partitions of finite vector spaces: an application of the Frobenius number in geometry
• On the size of a maximal partial spread
• On maximal partial spreads in \(PG\)(\(n\), \(q\))
• On a particular class of minihypers and its applications. I: The result for general \(q\)
• Nicht-einfache Partitionen endlicher Gruppen
• Finite nets. II: Uniqueness and imbedding
• On the finite group with a complete partition
• Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
• Partitions of the 8-dimensional vector space over GF(2)
• Group Partitions and Mixed Perfect Codes
• Maximal Strictly Partial Spreads
• Sets of Disjoint Lines in PG(3, q)
• Partial Spreads and Replaceable Nets
• Group Partition, Factorization and the Vector Covering Problem
• The Nonexistence of Certain Finite Projective Planes
• A maximal partial spread of size 45 in \(PG(3,7)\)