Almost affinely disjoint subspaces

In this work, we introduce a natural notion concerning finite vector spaces. A family of k-dimensional subspaces of Fqn, which forms a partial spread, is called almost affinely disjoint if any (k+1)-dimensional subspace containing a subspace from the family non-trivially intersects with only a few s...

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Bibliographic Details
Published in:Finite fields and their applications 2021-10, Vol.75, p.101879, Article 101879
Main Authors: Liu, Hedongliang, Polianskii, Nikita, Vorobyev, Ilya, Wachter-Zeh, Antonia
Format: Article
Language:English
Subjects:
Affinely disjoint subspaces
Partial spread
Subspace design
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Summary:In this work, we introduce a natural notion concerning finite vector spaces. A family of k-dimensional subspaces of Fqn, which forms a partial spread, is called almost affinely disjoint if any (k+1)-dimensional subspace containing a subspace from the family non-trivially intersects with only a few subspaces from the family. The central question discussed in the paper is the polynomial growth (in q) of the maximal cardinality of these families given the parameters k and n. For the cases k=1 and k=2, optimal families are constructed. For other settings, we find lower and upper bounds on the polynomial growth. Additionally, some connections with problems in coding theory are shown.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2021.101879