We study the average-case hardness of the class NP against algorithms in P. We prove that there exists some constant µ> 0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1 − (log n) −µ 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 + (log n) −µ 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 by a deterministic local decoder. error rate 1 4