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International Colloquium on Coding Theory and Applications

Coding Theory 1986: Coding Theory and Applications pp 19–32Cite as

Linear complexity in coding theory

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 311))

Abstract

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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References

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Author information

Authors and Affiliations

  1. Institute for Signal and Information Processing, Swiss Federal Institute of Technology, CH-8092, Zurich, Switzerland

    James L. Massey

  2. Central Laboratory, Landis & Gyr, CH-6301, Zug, Switzerland

    Thomas Schaub

Authors
  1. James L. Massey
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  2. Thomas Schaub
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Editor information

G. Cohen P. Godlewski

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© 1988 Springer-Verlag Berlin Heidelberg

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Massey, J.L., Schaub, T. (1988). Linear complexity in coding theory. In: Cohen, G., Godlewski, P. (eds) Coding Theory and Applications. Coding Theory 1986. Lecture Notes in Computer Science, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19368-5_2

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  • DOI: https://doi.org/10.1007/3-540-19368-5_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19368-5

  • Online ISBN: 978-3-540-39243-9

  • eBook Packages: Springer Book Archive

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