• DocumentCode
    896347
  • Title

    Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes

  • Author

    Carlet, Claude ; Mesnager, Sihem

  • Author_Institution
    Projet CODES, INRIA, Le Chesnay
  • Volume
    53
  • Issue
    1
  • fYear
    2007
  • Firstpage
    162
  • Lastpage
    173
  • Abstract
    By deriving bounds on character sums of Boolean functions and by using the characterizations, due to Kasami , of those elements of the Reed-Muller codes whose Hamming weights are smaller than twice and a half the minimum distance, we derive an improved upper bound on the covering radius of the Reed-Muller code of order 2, and we deduce improved upper bounds on the covering radii of the Reed-Muller codes of higher orders
  • Keywords
    Boolean functions; Hamming codes; Reed-Muller codes; binary codes; Boolean functions; Hamming weights; binary Reed-Muller codes; covering radius; upper bound; Australia; Boolean functions; Cryptography; Error correction codes; Hamming weight; Information theory; Maximum likelihood decoding; Measurement standards; Polynomials; Upper bound; Character sum; Reed–Muller codes; covering radius;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2006.887494
  • Filename
    4039651