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Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.

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Vector spaces over a field of prime order with certain hyperplanes

Let $V$ be a vector space of finite dimentional $d$ over a field of prime order $p$. For what values of $d$ and $p$, one can find $d+1$ (pairwise distinct) hyperplanes (subspaces of dimension $d-1$) $ …
Alireza Abdollahi's user avatar