Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects

Thomas Honold; Michael Kiermaier; Sascha Kurz

doi:10.1007/s00022-018-0459-6

Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects

Combinatorics 2018-12-17 v2

Authors: Thomas Honold , Michael Kiermaier , Sascha Kurz

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Abstract

In this article, the partial plane spreads in $PG(6,2)$ of maximum possible size $17$ and of size $16$ are classified. Based on this result, we obtain the classification of the following closely related combinatorial objects: Vector space partitions of $PG(6,2)$ of type $(3^{16} 4^1)$ , binary $3\times 4$ MRD codes of minimum rank distance $3$ , and subspace codes with parameters $(7,17,6)_2$ and $(7,34,5)_2$ .

Keywords

linear sets combinatorial designs

Cite

@article{arxiv.1606.07655,
  title  = {Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects},
  author = {Thomas Honold and Michael Kiermaier and Sascha Kurz},
  journal= {arXiv preprint arXiv:1606.07655},
  year   = {2018}
}

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31 pages, 9 tables

Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects

Abstract

Keywords

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