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Almost Affinely Disjoint Subspaces
- Source :
- Finite Fields and Their Applications, Volume 75, October 2021, 101879
- Publication Year :
- 2020
-
Abstract
- In this work, we introduce a natural notion concerning finite vector spaces. A family of $k$-dimensional subspaces of $\mathbb{F}_q^n$, 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.<br />Comment: 10 pages; Published in Finite Fields and Their Applications, Volume 75, October 2021, 101879
- Subjects :
- Mathematics - Combinatorics
Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Finite Fields and Their Applications, Volume 75, October 2021, 101879
- Publication Type :
- Report
- Accession number :
- edsarx.2007.01792
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.ffa.2021.101879