For non-negative integers $r\ge d$, how small can a subset $C\subset F_2^r$ be, given that for any $v\in F_2^r$ there is a $d$-flat passing through $v$ and contained in $C\cup\{v\}$? Equivalently, how large can a subset $B\subset F_2^r$ be, given that for any $v\in F_2^r$ there is a linear $d$-subspace not blocked non-trivially by the translate $B+v$? A number of lower and upper bounds are obtained.

Original language | English |
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Publisher | s.n. |
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Number of pages | 18 |
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Publication status | Published - 2013 |
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Name | arXiv.org |
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Volume | 1304.3233 [math.CO] |
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