On Pseudorandom Generators with Linear Stretch in NC0

. We consider the question of constructing cryptographic pseudorandom generators (PRGs) in NC 0 , namely ones in which each bit of the output depends on just a constant number of input bits. Previous constructions of such PRGs were limited to stretching a seed of n bits to n + o ( n ) bits. This leaves open the existence of a PRG with a linear (let alone superlinear) stretch in NC 0 . In this work we study this question and obtain the following main results: We show that the existence of a linear-stretch PRG in NC 0 implies non-trivial hardness of approximation results without relying on PCP machinery . In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. We construct a linear-stretch PRG in NC 0 under a specific intractability assumption related to the hardness of decoding “sparsely generated” linear codes. Such an assumption was previously conjectured by Alekhnovich (FOCS 2003).