  We present a simple deterministic gap-preserving reduction from SAT to the
Minimum Distance of Code Problem over $\F_2$. 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, which was recently derandomized by
Cheng and Wan. 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.
