• DocumentCode
    1410403
  • Title

    The Weights in MDS Codes

  • Author

    Ezerman, Martianus Frederic ; Grassl, Markus ; Solé, Patrick

  • Author_Institution
    Div. of Math. Sci., Nanyang Technol. Univ., Singapore, Singapore
  • Volume
    57
  • Issue
    1
  • fYear
    2011
  • Firstpage
    392
  • Lastpage
    396
  • Abstract
    The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code.
  • Keywords
    codes; MDS code; MDS conjecture; dual code; finite field; maximum distance separable code; Error correction codes; Linear code; Polynomials; Quantum mechanics; Rain; Vectors; Covering radius; MDS codes; quantum codes; weight distribution;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2010.2090246
  • Filename
    5673702
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1410403