On the Hardness of Approximating Balanced Homogenous 3-Lin

Johan Håstad, Rajsekar Manokaran
2017 Theory of Computing  
We consider systems of homogeneous linear equations modulo 2 with three variables in each equation and study balanced assignments as solutions to such equations. We prove that it is hard to distinguish systems where there is a balanced assignment that satisfies a fraction 1 − ε of the equations from systems where the best balanced assignment satisfies a fraction 1 2 + ε of the equations assuming that NP is not contained in quasipolynomial time. This improves on a similar result by Holmerin and
more » ... hot who relied on the assumption that NP is not contained in subexponential time. The key for the improvement is to replace long codes used by Holmerin and Khot by the low-degree long code.
doi:10.4086/toc.2017.v013a010 dblp:journals/toc/HastadM17 fatcat:bxo25zdlffdahl642bvk5ll2ti