• DocumentCode
    1449989
  • Title

    Some Results on Cyclic Codes Over {F}_{2}+v{F}_{2}

  • Author

    Zhu, Shixin ; Wang, Yu ; Shi, Minjia

  • Author_Institution
    Sch. of Math., Hefei Univ. of Technol., Hefei, China
  • Volume
    56
  • Issue
    4
  • fYear
    2010
  • fDate
    4/1/2010 12:00:00 AM
  • Firstpage
    1680
  • Lastpage
    1684
  • Abstract
    In this paper, we investigate the structure and properties of cyclic codes over the ring F 2+vF 2 . We first study the relationship between cyclic codes over F 2+vF 2 and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length n over F 2+vF 2.
  • Keywords
    cyclic codes; matrix algebra; polynomials; F2+vF2; binary cyclic codes; generator matrix; generator polynomial; gray map; Binary codes; Information theory; Laboratories; Linear code; Mathematics; Mobile communication; Modules (abstract algebra); Physics; Polynomials; Cyclic code; generator matrix; gray map; idempotent;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2010.2040896
  • Filename
    5437409
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1449989