• DocumentCode
    87907
  • Title

    An Improvement of the Gilbert–Varshamov Bound Over Nonprime Fields

  • Author

    Bassa, Alp ; Beelen, Peter ; Garcia, Alvaro ; Stichtenoth, Henning

  • Author_Institution
    Sabanci Univ., Istanbul, Turkey
  • Volume
    60
  • Issue
    7
  • fYear
    2014
  • fDate
    Jul-14
  • Firstpage
    3859
  • Lastpage
    3861
  • Abstract
    The Gilbert-Varshamov bound guarantees the existence of families of codes over the finite field Fℓ with good asymptotic parameters. We show that this bound can be improved for all nonprime fields Fℓ with ℓ ≥ 49 , except possibly ℓ = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes.
  • Keywords
    Goppa codes; algebraic codes; orthogonal codes; Gilbert-Varshamov bound; Goppa algebraic geometry codes; nonprime fields; self-orthogonal codes; transitive codes; Educational institutions; Electronic mail; Geometry; Linear codes; Poles and towers; AG codes; GV bound; towers of function fields;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2014.2316531
  • Filename
    6803057
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=87907