• DocumentCode
    77345
  • Title

    On the Covering Radius of First-Order Generalized Reed–Muller Codes

  • Author

    Leducq, E.

  • Author_Institution
    Inst. de Math. de Jussieu, Univ. Paris Diderot, Paris, France
  • Volume
    59
  • Issue
    3
  • fYear
    2013
  • fDate
    Mar-13
  • Firstpage
    1590
  • Lastpage
    1596
  • Abstract
    We generalize to any finite Fq fields a theorem about covering radius of codes of strength 2 proved by Helleseth and coworkers. Then,using this result and partial covering radius, we give bounds for the covering radius of first-order generalized Reed-Muller codes. Finally, using Magma, we get some improvements for F3.
  • Keywords
    Reed-Muller codes; first-order generalized Reed-Muller codes; partial covering radius; Binary codes; Frequency modulation; Hamming weight; Indexes; Kernel; Polynomials; Upper bound; Covering radius; generalized Reed–Muller codes;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2012.2230216
  • Filename
    6362214
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=77345