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LEMMA: Let X be any vector (not all zeros) in Z2n. Let R be a random vector over Z2n. Then Pr[X.R = 0] ≤ 1/2 |
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LEMMA: Let X be any vector (not all zeros) in Z2n. Let R be a random vector over Z2n. Then Pr[X\cdot R = 0] ≤ 1/2. PROOF: Fix X. Let i be an index such that Xi\neq 0. |
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PROOF: Fix X. Let i be an index such that Xi≠ 0. |
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{R\cdot X, F(R)\cdot X} |
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{R.X, F(R).X} |
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Note X.R = ∑i Xi Ri (mod 2). |
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