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

  • Per Austrin
  • Subhash Khot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

We present a simple deterministic gap-preserving reduction from SAT to the Minimum Distance of Code Problem over \(\mathbb{F}_2\). 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.

Keywords

Linear Code Pseudorandom Generator Consistency Constraint Good Code Code Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Per Austrin
    • 1
  • Subhash Khot
    • 2
  1. 1.University of TorontoCanada
  2. 2.New York UniversityUSA

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