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Olof Heden, in his work "A survey of the different types of vector space partitions", discusses various results regarding the following qustion - given a vector space $V$ over a finite field, how can we partition it into a set $\mathcal P$ of vector spaces, such that every $v\in V,v\ne 0$ belongs to exactly one member of $\mathcal P$? I'm interseted in a generalization of this work to covering any general subset of a vector space over a finite field by not only vector spaces, but also affine spaces. Is anyone familiar with a work done on this subject?

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Do you have any restrictions on the kind of covering you want (minimum number of spaces, say?) After all, every single point of $F_q^n$ is an affine subspace. – Klaus Draeger Feb 27 '12 at 13:52
Ofcourse. I'm looking for the minimum cover. Although any other result could be useful as well. – Netanel Feb 28 '12 at 9:28

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