• DocumentCode
    1025797
  • Title

    On the Minimum Distance Conjecture for Schubert Codes

  • Author

    Xiang, Xu

  • Author_Institution
    GuangZhou Univ., Guangzhou
  • Volume
    54
  • Issue
    1
  • fYear
    2008
  • Firstpage
    486
  • Lastpage
    488
  • Abstract
    In 2000, S. R. Ghorpade and G. Lachaud presented a conjecture on the minimum distance of algebraic geometric codes associated to Schubert varieties. In this correspondence, we use the structure and properties of the exterior algebra to give an elementary proof of this conjecture, and provide a construction of codewords of minimum Hamming weight.
  • Keywords
    Hamming codes; algebraic codes; Schubert codes; algebraic codes; codewords; exterior algebra; geometric codes; minimum Hamming weight; minimum distance conjecture; Algebra; Codes; Galois fields; Hamming weight; Mathematics; Software engineering; Linear code; Schubert variety; minimum distance; projective space; wedge product;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2007.911283
  • Filename
    4418507
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1025797