• DocumentCode
    1766513
  • Title

    Generalized Hamming Weights of Irreducible Cyclic Codes

  • Author

    Minghui Yang ; Jin Li ; Keqin Feng ; Dongdai Lin

  • Author_Institution
    State Key Lab. of Inf. Security, Inst. of Inf. Eng., Beijing, China
  • Volume
    61
  • Issue
    9
  • fYear
    2015
  • fDate
    Sept. 2015
  • Firstpage
    4905
  • Lastpage
    4913
  • Abstract
    The generalized Hamming weights dr(C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[=d1(C)] and have become an important research object in coding theory since Wei´s originary work in 1991. In this paper, two general formulas on d(C) for irreducible cyclic codes are presented using Gauss sums and the weight hierarchy {d1(C), d2(C), ... , dk(C)} (k= dim C) is completely determined for several cases.
  • Keywords
    Hamming codes; cyclic codes; linear codes; number theory; Gauss sums; coding theory; generalized Hamming weights; irreducible cyclic codes; linear code; natural minimum Hamming distance generalization; weight hierarchy; Additives; Hamming distance; Hamming weight; Linear codes; Next generation networking; Polynomials; Gauss sum; Generalized Hamming weight; generalized Hamming weight; irreducible cyclic code;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2015.2444013
  • Filename
    7126992
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1766513