# 2018-13 Bernoulli vectors

Assume that $$x \in \mathbb{R}^n$$ with at least $$k$$ non-zero entries $$( k> 0 )$$. Let
$A = \{ y \in \{-1, 1\}^n : y \cdot x = 0 \}.$
Prove that $$|A| \leq k^{-1/2} 2^n$$.

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