• DocumentCode
    873262
  • Title

    Codes over algebraic integer rings of cyclotomic fields

  • Author

    Fan, Yun ; Gao, Ying

  • Author_Institution
    Dept. of Math., Wuhan Univ., China
  • Volume
    50
  • Issue
    1
  • fYear
    2004
  • Firstpage
    194
  • Lastpage
    200
  • Abstract
    Regarding any finite field as a residue field of the algebraic integer ring of a cyclotomic field, we select a system of representatives in the ring with minimal Manhattan metric, and introduce a Mannheim weight on the finite field. The linear codes over the finite field with the Mannheim weight are discussed. A geometric method to compute the representatives in Gaussian integers is provided.
  • Keywords
    Gaussian distribution; algebraic geometric codes; linear codes; minimisation; Gaussian integer representatives; Mannheim weight; algebraic integer ring; cyclotomic field; finite field; geometric method; linear codes; minimal Manhattan metric; residue field; Constellation diagram; Error correction; Error correction codes; Euclidean distance; Galois fields; Lattices; Linear code; Mathematics; Multidimensional systems;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2003.821983
  • Filename
    1262628