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A Simple Deterministic Reduction for the Gap Minimum Distance of Code Problem
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0001-8217-0158
2014 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, Vol. 60, no 10, 6636-6645 p.Article in journal (Refereed) Published
Abstract [en]

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 fixed 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 nontrivial coding theoretic constructions, whereas our reduction is elementary. As an additional feature, our reduction gives hardness within a constant factor even for asymptotically good codes, i.e., having constant positive rate and relative distance. Previously, it was not known how to achieve a deterministic reduction for such codes.

Place, publisher, year, edition, pages
2014. Vol. 60, no 10, 6636-6645 p.
Keyword [en]
Linear code, computational complexity
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-154750DOI: 10.1109/TIT.2014.2340869ISI: 000342416900048ScopusID: 2-s2.0-84907221430OAI: diva2:761072

QC 20141105

Available from: 2014-11-05 Created: 2014-10-27 Last updated: 2015-02-02Bibliographically approved

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Austrin, Per
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