• DocumentCode
    1401616
  • Title

    The intractability of computing the minimum distance of a code

  • Author

    Vardy, Alexander

  • Author_Institution
    Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA
  • Volume
    43
  • Issue
    6
  • fYear
    1997
  • fDate
    11/1/1997 12:00:00 AM
  • Firstpage
    1757
  • Lastpage
    1766
  • Abstract
    It is shown that the problem of computing the minimum distance of a binary linear code is NP-hard, and the corresponding decision problem is NP-complete. This result constitutes a proof of the conjecture of Berlekamp, McEliece, and van Tilborg (1978). Extensions and applications of this result to other problems in coding theory are discussed
  • Keywords
    computational complexity; decision theory; linear codes; Berlekamp McEliece and van Tilborg conjecture; NP-complete problem; NP-hard problem; binary linear code; coding theory; decision problem; minimum distance; Combinatorial mathematics; Distributed computing; History; Linear code; Maximum likelihood decoding; NP-complete problem; Parity check codes; Polynomials; Turing machines; Vectors;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.641542
  • Filename
    641542
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1401616