Designs, Codes and Cryptography

, Volume 85, Issue 1, pp 97–106 | Cite as

Improved upper bounds for partial spreads

Article

Abstract

A partial \((k-1)\)-spread in \({\text {PG}}(n-1,q)\) is a collection of \((k-1)\)-dimensional subspaces with trivial intersection. So far, the maximum size of a partial \((k-1)\)-spread in \({\text {PG}}(n-1,q)\) was known for the cases \(n\equiv 0\pmod k\), \(n\equiv 1\pmod k\), and \(n\equiv 2\pmod k\) with the additional requirements \(q=2\) and \(k=3\). We completely resolve the case \(n\equiv 2\pmod k\) for the binary case \(q=2\).

Keywords

Galois geometry Partial spreads Constant dimension codes Vector space partitions Orthogonal arrays \((s , r , \mu )\)-nets 

Mathematics Subject Classification

51E23 05B15 05B40 11T71 94B25 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BayreuthBayreuthGermany

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