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Number of points covered by $2n$ hyperplanes in $\mathbf{F}_p^n$

For a prime $p$, fix two bases $U=\{v_1,\dots,v_n\}$ and $W=\{w_1,\dots,w_n\}$ of the vector space $V=\mathbf{F}_p^n$. We may assume $U$ is the standard basis without loss of generality. For $s_1,\dot …
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