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On sumsets and translates of vector subspaces over finite fields. (Chinese. English summary) Zbl 1413.11018

Summary: Let \(\mathcal{F}_p^n\) be a finite field model and \(B \subset \mathcal{F}_p^n\), it is shown that there exist a vector subspace \(V\) and a constant \(D > 0\) such that dim \(V \geq D\) and \(A + B\) contains a translate of the subspace \(V\).

MSC:

11B13 Additive bases, including sumsets
51D20 Combinatorial geometries and geometric closure systems
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