Almost affinely disjoint subspaces

Hedongliang Liu, Nikita Polianskii, Ilya Vorobyev, Antonia Wachter-Zeh

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Article number101879
JournalFinite Fields and their Applications
Publication statusPublished - Oct 2021


  • Affinely disjoint subspaces
  • Partial spread
  • Subspace design


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