Linear complexity in coding theory

  • James L. Massey
  • Thomas Schaub
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 311)


The linear complexity of sequences is defined and its main properties reviewed. The linear complexity of periodic sequences is examined in detail and an extensive list of its properties is formulated. The discrete Fourier transform (DFT) of a finite sequence is then connected to the linear complexity of a periodic sequence by Blahut's theorem. Cyclic codes are given a DFT formulation that relates their minimum distance to the least linear complexity among certain periodic sequences. To illustrate the power of this approach, a slight generalization of the Hartmann-Tzeng lower bound on minimum distance is proved, as well as the Bose-Chaudhuri-Hocquenghem lower bound. Other applications of linear complexity in the theory of cyclic codes are indicated.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • James L. Massey
    • 1
  • Thomas Schaub
    • 2
  1. 1.Institute for Signal and Information ProcessingSwiss Federal Institute of TechnologyZurichSwitzerland
  2. 2.Central LaboratoryLandis & GyrZugSwitzerland

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