• DocumentCode
    1298187
  • Title

    A Lower Bound on the Optimum Distance Profiles of the Second-Order Reed–Muller Codes

  • Author

    Chen, Yanling ; Vinck, A. J Han

  • Author_Institution
    Fraunhofer IESE, Kaiserslautern, Germany
  • Volume
    56
  • Issue
    9
  • fYear
    2010
  • Firstpage
    4309
  • Lastpage
    4320
  • Abstract
    In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed-Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed-Muller codes of length ≤ 256. We show that the bound is tight in both orders for the codes of length ≤ 128 .
  • Keywords
    Reed-Muller codes; matrix algebra; inverse dictionary order; lower bound; optimum distance profiles; second-order reed-muller codes; symplectic matrix; Block codes; Boolean functions; Channel coding; Decoding; Dictionaries; Distance measurement; Error correction; Error correction codes; Generators; Linear code; Mathematics; Polarization; Upper bound; Boolean function; MacWilliams´ identities; Reed–Muller code; optimum distance profile; symplectic matrix;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2010.2054512
  • Filename
    5550502
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1298187