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Results tagged with finite-geometry
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user 34180
Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.
5
votes
Accepted
$(n-2)$-blocking sets in $AG(n,2)$
Not much is known for the general case.
Let $m(k, n, q)$ denote the minimum size of an $k$-blocking set in $AG(n, q)$. Trivially we have $m(0, n, q) = q^n$ and $m(n, n, q) = 1$. By Jamison/Brouwer-S …
- 1,197
3
votes
Blocking sets in three dimensional finite affine spaces
Here is an improvement of the upper bound which I found in ``The polynomial method in Galois geometries'' by Simeon Ball. See page number 4.
The known constructions are somewhat crude. For exampl …
- 1,197
3
votes
On MDS code property
It has been proved by Simeon Ball that for $k \leq p$, all $[n, k, n-k+1]_q$ codes are Reed-Solomon codes, where $q = p^h$. See Corollary 9.2 in the following paper:
Ball, S. On sets of vectors of a …
- 1,197
2
votes
Covering all, but $k$ points with affine subspaces
Here are some partial answers to your question.
Let $A = A_1 \times \dots \times A_n \subseteq F^n$ be a finite grid.
Alon and Furedi proved that you need at least $\sum (\# A - 1)$ hyperplanes to …
- 1,197
2
votes
Are bipartite Moore graphs Hamiltonian?
This recent paper of Sato and Suzuki shows that the graphs corresponding to some classical generalized quadrangles are indeed Hamiltonian:
Sato, H. & Suzuki, H. Graphs and Combinatorics (2018). http …
- 1,197