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

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Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Classification of large partial plane spreads in PG(6,2) and related combinatorial objects.
In: Journal of Geometry. Bd. 110 (2019) . - 5.
ISSN 1420-8997
DOI: https://doi.org/10.1007/s00022-018-0459-6

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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 3x4 MRD codes of minimum rank distance 3, and subspace codes with parameters (7,17,6)_2 and (7,34,5)_2.