Proves NP-hardness of distinguishing value 1-δ vs at most 1/q^{1-ε} for 2P1R projection games with large alphabet q (power of 2), improving the alphabet-soundness tradeoff over prior work.
That is,QandWsatisfydim(Q)+codim(W) = rand there exists linearg Q,W :W→F q such that Pr L∈Grass(n,2ℓ) [gQ,W |L = eT1[L]|Q⊆L⊆W]⩾ε ′ :=q −2(1−1000δ2)ℓ
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Near Optimal Alphabet-Soundness Tradeoff PCPs
Proves NP-hardness of distinguishing value 1-δ vs at most 1/q^{1-ε} for 2P1R projection games with large alphabet q (power of 2), improving the alphabet-soundness tradeoff over prior work.