Lecture 16 : Hardness of E 3 - LIN 2 , Håstad ’ s 3 - query PCP

We begin with a long code test, where our goal is that functions which pass this test with high probability are close to a linear function with small support. We do this by examining our old linearity test but add in a bit of noise, in the form a string μ. This little bit of noise will allow us to conclude that the support for the function is small and further is under the control of out and δ parameters. Definition 2.1. We say a string μ ∈ {−1, 1} is picked randomly with bias if for each i. μi = { 1 with prob 1− 2 −1 with prob 2 .