• DocumentCode
    1523516
  • Title

    Finding the defining functions for one-point algebraic-geometry codes

  • Author

    Leonard, Douglas A.

  • Author_Institution
    Dept. of Discrete & Stat. Sci., Auburn Univ., AL, USA
  • Volume
    47
  • Issue
    6
  • fYear
    2001
  • fDate
    9/1/2001 12:00:00 AM
  • Firstpage
    2566
  • Lastpage
    2573
  • Abstract
    An iterative algorithm is given for producing the parity-check functions for one-point algebraic-geometry (AG) codes, in particular (but not limited to) those related to the two towers of function fields introduced by Garcia and Stichtenoth (1995). This simple method, based on the linearity of the Qth-power map over FQ, is an alternative to the method of using Laurent series expansions. Examples are given for small values of m with characteristic p=2 for both towers
  • Keywords
    algebraic geometric codes; functions; iterative methods; Qth-power map; defining functions; iterative algorithm; one-point algebraic-geometry codes; parity-check functions; towers of function fields; Equations; Heart; Iterative algorithms; Linearity; Parity check codes; Poles and towers; Polynomials; Pulp and paper industry;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.945271
  • Filename
    945271
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1523516