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Combinatorica

, Volume 6, Issue 3, pp 275–278 | Cite as

On the non-existence of barker sequences

  • Michele Elia
Article

Abstract

It is an old conjecture that there are no unknown Barker sequences. Here, a sufficient condition for the non-existence of Barker sequences of even length 4m 2 is given, which allows us to show that there are no unknown sequences withm less than 105, exceptm=63, which remains still undecided.

AMS subject classification (1980)

05 B 99 

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References

  1. [1]
    R. H. Barker, Group synchronizing of binary digital systems, in:Communication Theory, (W. Jackson, ed.), Academic Press, New York, (1953), 273–287.Google Scholar
  2. [2]
    L. D. Baumert,Cyclic Difference Sets, Springer Verlag, New York, (1971).zbMATHGoogle Scholar
  3. [3]
    T. W. Hungerford,Algebra, Springer-Verlag, New York, (1980).zbMATHGoogle Scholar
  4. [4]
    R. Turyn andJ. Storer, On binary sequences,Proc. Am. Math. Soc.,12 (1961), 394–399.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • Michele Elia
    • 1
  1. 1.Instituto Matematico Politecnico di TorinoItaly

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