• DocumentCode
    1418632
  • Title

    Orphans of the first order Reed-Muller codes

  • Author

    Brualdi, Richard A. ; Pless, Vera S.

  • Author_Institution
    Dept. of Math., Wisconsin Univ., Madison, WI, USA
  • Volume
    36
  • Issue
    2
  • fYear
    1990
  • fDate
    3/1/1990 12:00:00 AM
  • Firstpage
    399
  • Lastpage
    401
  • Abstract
    If C is a code, an orphan is a coset that is not a descendant. Orphans arise naturally in the investigation of the covering radius. Case C has only even-weight vectors and minimum distance of at least four. Cosets that are orphans are characterized, and then the existence is proved of a family of orphans of first-order Reed-Muller codes R(1, m). For m⩽5 all orphans of R(1, m) are identified
  • Keywords
    error correction codes; Reed-Muller codes; binary linear codes; coset; covering radius; even-weight vectors; first order codes; minimum distance; orphan; Distributed computing; Linear code; Mathematics; Vectors;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.52488
  • Filename
    52488
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1418632