# Seminar: February 11, 10am, Room 277

## Subhash Khot, New York University

## A Simple Deterministic Reduction for the Gap Minimum Distance of Code Problem

We present a simple deterministic gap-preserving reduction from SAT to the Minimum Distance of Code Problem over GF(2). We also show how to extend the reduction to work over any finite field. Previously a randomized reduction was known due to Dumer, Micciancio, and Sudan [1999], which was recently derandomized by Cheng and Wan [2009]. These reductions rely on highly non-trivial coding theoretic constructions whereas our reduction is elementary.

As an additional feature, our reduction gives a constant factor hardness even for asymptotically good codes, i.e., having constant rate and relative distance. Previously it was not known how to achieve deterministic reductions for such codes.

Joint work with Per Austrin.