Hardness amplification within NP against deterministic algorithms

We study the average-case hardness of the class NP against algorithms in P. We prove that there exists some constant @m>0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1-(logn)^-^@m fraction of inputs of length n, then there is a language L^' in NP for which no deterministic polynomial time algorithm can decide L^' correctly on a 3/4+(logn)^-^@m fraction of inputs of length n. In coding theoretic terms, we give a construction of a monotone code that can be uniquely decoded up to error rate 14 by a deterministic local decoder.

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