Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Approximating the SVP to within a factor (1+1/dimE) is NP-Hard under randomized reductions
Journal of Computer and System Sciences
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Hardness of Approximating the Minimum Distance of a Linear Code
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Hardness of Approximating the Shortest Vector Problem in High Lp Norms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness of Approximating the Shortest Vector Problem in Lattices
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Complexity of Decoding Positive-Rate Reed-Solomon Codes
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A deterministic reduction for the gap minimum distance problem: [extended abstract]
Proceedings of the forty-first annual ACM symposium on Theory of computing
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
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We present a simple deterministic gap-preserving reduction from SAT to the Minimum Distance of Code Problem over F2. 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.