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An Improved Approximation Algorithm for Computing the k-Error Linear Complexity of Sequences Using the Discrete Fourier Transform

  • Ana Sălăgean
  • Alexandra Alecu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)

Abstract

In our previous work we transformed the optimisation problem of finding the k-error linear complexity of a sequence into an optimisation problem in the DFT (Discrete Fourier Transform) domain, using Blahut’s theorem. We then gave an approximation algorithm of polynomial complexity for the transformed problem by restricting the search space to error sequences whose DFT have period up to k. However, when applying the inverse transformation, the error vectors obtained are in general in an extension of the original field.

In the present paper we develop our previous approximation algorithm so that now it can be constrained to only obtain errors over the original field. Essentially, we give a polynomial approximation algorithm for the computation of the k-error linear complexity of a sequence. More precisely, the algorithm will find the optimum among a restricted set of errors over the original field. While this restricted search space is still exponential, the complexity of the algorithm is polynomial, \({\mathcal{O}}(N^2\log N \log \log N)\).

Keywords

periodic sequences linear complexity k-error linear complexity discrete Fourier transform 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ana Sălăgean
    • 1
  • Alexandra Alecu
    • 2
  1. 1.Department of Computer ScienceLoughborough UniversityUK
  2. 2.Google, Inc.ZürichSwitzerland

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