We present a simple deterministic gap-preserving reduction from SAT to the Minimum Distance of Code Problem over . We also show how to extend the reduction to work over any finite field (of constant size). Previously a randomized reduction was known due to Dumer, Micciancio, and Sudan [9], which was recently derandomized by Cheng and Wan [7, 8]. 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. © 2011 Springer-Verlag.
CITATION STYLE
Austrin, P., & Khot, S. (2011). A simple deterministic reduction for the gap minimum distance of code problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6755 LNCS, pp. 474–485). https://doi.org/10.1007/978-3-642-22006-7_40
Mendeley helps you to discover research relevant for your work.