• DocumentCode
    271356
  • Title

    New Lower Bounds on the Generalized Hamming Weights of AG Codes

  • Author

    Bras-Amorós, Maria ; Kwankyu Lee ; Vico-Oton, Albert

  • Author_Institution
    Dept. of Comput. Eng. & Math., Univ. Rovira i Virgili, Tarragona, Spain
  • Volume
    60
  • Issue
    10
  • fYear
    2014
  • fDate
    Oct. 2014
  • Firstpage
    5930
  • Lastpage
    5937
  • Abstract
    A sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized. Then, the result is used, through the so-called Feng-Rao numbers, to bound the generalized Hamming weights of algebraic-geometry codes. This is further developed for Hermitian codes and the codes on one of the Garcia-Stichtenoth towers, as well as for some more general families.
  • Keywords
    Hamming codes; Hermitian matrices; algebraic codes; geometric codes; AG codes; Feng-Rao numbers; Garcia-Stichtenoth towers; Hermitian codes; algebraic-geometry codes; generalized Hamming weights; Conductors; Erbium; Hamming weight; Linear codes; Poles and towers; Upper bound; AG code; Feng-Rao number; Garcia-Stichtenoth towers; Hermitian codes; Numerical semigroup; generalized Hamming weights; ideal of a semigroup; isometry-dual sets of AG codes; order bound;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2014.2343993
  • Filename
    6867350
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=271356