• DocumentCode
    771738
  • Title

    Quasi-cyclic codes over Z4 and some new binary codes

  • Author

    Aydin, Nuh ; Ray-Chaudhuri, Dwijendra K.

  • Author_Institution
    Dept. of Math., Ohio State Univ., Columbus, OH, USA
  • Volume
    48
  • Issue
    7
  • fYear
    2002
  • fDate
    7/1/2002 12:00:00 AM
  • Firstpage
    2065
  • Lastpage
    2069
  • Abstract
    Previously, (linear) codes over Z4 and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z 4-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z4 produces a new binary code, a (92, 224, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials
  • Keywords
    Galois fields; binary codes; cyclic codes; linear codes; nonlinear codes; polynomials; Galois field; Golay code; Gray map; Z4-QC codes; binary codes; coding theory; cyclic codes; finite fields; free modules; generator polynomials; linear codes; nonlinear codes; quasi-cyclic codes; Binary codes; Galois fields; Linear code; Mathematics; Web sites;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2002.1013145
  • Filename
    1013145
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=771738