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An upper bound on the number of sets of parallel lines covering points in a finite plane?
Let $\mathbb{F}$ be a finite field of characteristic $2$. Let $L_m$ denote the set of lines in $\mathbb{F}^2$ with slope $m\in\mathbb{F}$, that is, all parallel lines of the form $y=mx+b$. Consider a ...
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1
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Finding a set of disjoint affine subspaces such that their union is equal to a given subset of $\mathbb{F}_2^n$
Suppose I'm given a set of point $S = \{x_1, \dots, x_m \} \subseteq \mathbb{F}_2^n$, and the following task. Find a set of disjoint affine subspaces of $\mathbb{F}_2^n$, $A_1, \dots, A_k$ satisfying ...
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