• DocumentCode
    1311684
  • Title

    Linearized Shift-Register Synthesis

  • Author

    Sidorenko, Vladimir ; Richter, Gerd ; Bossert, Martin

  • Author_Institution
    Inst. of Telecommun. & Appl. Inf. Theor., Ulm Univ., Ulm, Germany
  • Volume
    57
  • Issue
    9
  • fYear
    2011
  • Firstpage
    6025
  • Lastpage
    6032
  • Abstract
    An efficient algorithm synthesizing all shortest q -linearized-feedback shift-registers generating a given sequence of length N over a finite field BBFqm is derived and its correctness is proved. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity O(lN) <;~O(N2) operations in BBFqm, where l is the linearized complexity of the sequence. The algorithm can be applied for efficiently solving the key equation when decoding Gabidulin codes.
  • Keywords
    decoding; shift registers; Berlekamp-Massey algorithm; Gabidulin codes; q-linearized-feedback shift-registers; Algorithm design and analysis; Complexity theory; Decoding; Linear algebra; Polynomials; Registers; Gabidulin codes; key equation; linearized complexity; linearized-feedback; shift-register synthesis;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2011.2162173
  • Filename
    6006607
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1311684