Improved upper bounds for partial spreads

DOI10.1007/s10623-016-0290-8zbMath1378.51010arXiv1512.04297OpenAlexW3104527030MaRDI QIDQ2402972

Sascha Kurz

Publication date: 15 September 2017

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

Full work available at URL: https://arxiv.org/abs/1512.04297

zbMATH Keywords

orthogonal arrayspartial spreadsGalois geometryvector space partitionsconstant dimension codes\((s , r , \mu )\)-nets

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Orthogonal arrays, Latin squares, Room squares (05B15) Spreads and packing problems in finite geometry (51E23) Combinatorial codes (94B25) Combinatorial aspects of packing and covering (05B40)

Related Items (10)

Almost affinely disjoint subspaces and covering Grassmannian codes ⋮ Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6 ⋮ 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 ⋮ Generalized vector space partitions ⋮ Optimal Binary Linear Locally Repairable Codes with Disjoint Repair Groups ⋮ Johnson type bounds for mixed dimension subspace codes ⋮ An asymptotically optimal construction of almost affinely disjoint subspaces ⋮ Flag codes: distance vectors and cardinality bounds

Cites Work

• The supertail of a subspace partition
• The maximum size of a partial spread. II: Upper bounds
• The maximum size of a partial 3-spread in a finite vector space over \(\mathrm{GF}(2)\)
• Galois geometries and coding theory
• On the length of the tail of a vector space partition
• Theory of codes with maximum rank distance
• Partial t-spreads and group constructible \((s,r,\mu)\)-nets
• Partial spreads in finite projective spaces and partial designs
• Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6
• Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
• A Rank-Metric Approach to Error Control in Random Network Coding
• Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams
• Recursive Code Construction for Random Networks
• A General Class of Maximal Codes ror Computer Applications

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