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On the inherent intractability of certain coding problems

Berlekamp, Elwyn R. and McEliece, Robert J. and van Tilborg, Henk C. A. (1978) On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory, 24 (3). pp. 384-386. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:BERieeetit78

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Abstract

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.


Item Type:Article
Additional Information:© Copyright 1978 IEEE. Reprinted with permission. Manuscript received March 2, 1977; revised September 14, 1977. The contribution of McEliece and van Tilborg to this correspondence represents one phase of research sponsored by the National Aeronautics and Space Administration under Contract No. NAS7-100, carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA. We wish to thank one of the referees for pointing out to us the relation between the "weight ≤ w" decision problem and the minimum weight problem for linear codes.
Record Number:CaltechAUTHORS:BERieeetit78
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BERieeetit78
Alternative URL:http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=22702&arnumber=1055873&count=24&index=1
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ID Code:5607
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Oct 2006
Last Modified:26 Dec 2012 09:13

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