• DocumentCode
    1412867
  • Title

    The weight hierarchy of product codes

  • Author

    Schaathun, Hans Georg

  • Author_Institution
    Dept. of Inf., Bergen Univ., Norway
  • Volume
    46
  • Issue
    7
  • fYear
    2000
  • fDate
    11/1/2000 12:00:00 AM
  • Firstpage
    2648
  • Lastpage
    2651
  • Abstract
    The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang (1993) gave a conjecture about the minimum weights for some product codes. In this article, we find a relation between product codes and the Segre embedding of a pair of projective systems, and we use this to prove the conjecture
  • Keywords
    linear codes; set theory; Segre embedding; coordinate positions; linear code; minimum weight; minimum weights; product codes; projective multiset; projective systems; subcode; weight hierarchy; Informatics; Linear code; Product codes; Tensile stress; Vectors;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.887876
  • Filename
    887876
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1412867