• DocumentCode
    3084754
  • Title

    Polynomial codes and principal ideal rings

  • Author

    Cazaran, Jilyana ; Kelarev, Andrei V.

  • Author_Institution
    Dept. of Math., Tasmania Univ., Hobart, Tas., Australia
  • fYear
    1997
  • fDate
    29 Jun-4 Jul 1997
  • Firstpage
    502
  • Abstract
    Conditions are given which determine when the ring R=S[x1 , ..., xn]/(f1(x1), ..., fn (xn)) is a principal ideal ring where either S=Z m and R is finite or S is a field. If S and R are both finite then an ideal C of R is a linear code. Hence one obtains necessary and sufficient conditions for the existence of a single generator polynomial of C. If S is a finite field and fi(x i)=xili-1 for certain integers li for i=1 to n then the ideals of R are multivariate cyclic codes and include the class of generalized Reed-Muller codes
  • Keywords
    Reed-Muller codes; cyclic codes; linear codes; polynomials; finite field; generalized Reed-Muller codes; linear code; multivariate cyclic codes; polynomial codes; principal ideal rings; single generator polynomial; Australia; Galois fields; Hamming distance; Linear code; Mathematics; Polynomials; Sufficient conditions;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on
  • Conference_Location
    Ulm
  • Print_ISBN
    0-7803-3956-8
  • Type

    conf

  • DOI
    10.1109/ISIT.1997.613439
  • Filename
    613439
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3084754