Designs, Codes and Cryptography

, Volume 80, Issue 2, pp 409–414 | Cite as

Barker sequences of odd length

  • Kai-Uwe SchmidtEmail author
  • Jürgen Willms


A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn asserts that there is no Barker sequence of length greater than 13. In 1961, Turyn and Storer gave an elementary, though somewhat complicated, proof that this conjecture holds for odd lengths. We give a new and simpler proof of this result.


Aperiodic autocorrelation Barker sequence Binary sequence 

Mathematics Subject Classification

11B83 05B10 94A55 



K.-U. Schmidt was supported by German Research Foundation (DFG).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of MathematicsOtto-von-Guericke UniversityMagdeburgGermany
  2. 2.Institut für Computer Science, Vision and Computational IntelligenceFachhochschule SüdwestfalenMeschedeGermany

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