Appended m-Sequences with Merit Factor Greater than 3.34

  • Jonathan Jedwab
  • Kai-Uwe Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


We consider the merit factor of binary sequences obtained by appending an initial fraction of an m-sequence to itself. We show that, for all sufficiently large n, there is some rotation of each m-sequence of length n that has merit factor greater than 3.34 under suitable appending. This is the first proof that the asymptotic merit factor of a binary sequence family can be increased under appending. We also conjecture, based on numerical evidence, that each rotation of an m-sequence has asymptotic merit factor greater than 3.34 under suitable appending. Our results indicate that the effect of appending on the merit factor is strikingly similar for m-sequences as for rotated Legendre sequences.


Binary Sequence Numerical Evidence Primitive Element Initial Fraction Merit Factor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jonathan Jedwab
    • 1
  • Kai-Uwe Schmidt
    • 1
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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