TY - GEN

T1 - A simple deterministic reduction for the gap minimum distance of code problem

AU - Austrin, Per

AU - Khot, Subhash

N1 - Funding Information:
Research done while first author at New York University supported by NSF Expeditions grant CCF-0832795. Second author supported by NSF CAREER grant CCF-0833228, NSF Expeditions grant CCF-0832795, and BSF grant 2008059.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-22006-7_40

DO - 10.1007/978-3-642-22006-7_40

M3 - Conference contribution

AN - SCOPUS:79959926615

SN - 9783642220050

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 474

EP - 485

BT - Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings

T2 - 38th International Colloquium on Automata, Languages and Programming, ICALP 2011

Y2 - 4 July 2011 through 8 July 2011

ER -