• DocumentCode
    2392396
  • Title

    Grobner bases and alternant codes over Galois rings

  • Author

    Byrne, Eimear ; Fitzpatrick, Patrick

  • Author_Institution
    Dept. of Math, Nat. Univ. of Ireland, Cork, Ireland
  • fYear
    2000
  • fDate
    2000
  • Firstpage
    448
  • Abstract
    We give a new algorithm for the solution of the Hamming metric decoding problem for alternant codes over a Galois ring R. First we develop a comprehensive theory of Grobner bases over R|x1,...,xn|, which is of independent interest. By specialising to the case of one variable, we show that the solution of the key equation can be determined as a certain minimal element in a Grobner basis of the solution module
  • Keywords
    Galois fields; codes; decoding; polynomials; Galois rings; Grobner bases; Hamming metric decoding; alternant codes; key equation; Analog computers; Decoding; Equations; Hamming distance; Interpolation; Mathematics; Parity check codes; Polynomials;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Information Theory, 2000. Proceedings. IEEE International Symposium on
  • Conference_Location
    Sorrento
  • Print_ISBN
    0-7803-5857-0
  • Type

    conf

  • DOI
    10.1109/ISIT.2000.866746
  • Filename
    866746
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2392396