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A091704 Number of Barker codes (or Barker sequences) of length n up to reversals and negations. 4
2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

It is conjectured that there are no Barker codes of length > 13.

If there are any nonzero terms for n > 13, they are either at n = 3979201339721749133016171583224100 or at n larger than 4 * 10^33 (Borwein & Mossinghoff, 2014). - Felix Fröhlich, Feb 08 2017

REFERENCES

R. H. Barker, Group synchronizing of binary digital sequences, in "Communication Theory", Butterworth, London, 1953, pp. 273-287.

H. D. Lueke, Korrelationssignale, Springer 1992.

LINKS

Table of n, a(n) for n=2..103.

Peter Borwein and Tamas Erdelyi, A note on Barker polynomials, arXiv:1206.5371 [math.NT], 2012.

P. Borwein and M. J. Mossinghoff, Wieferich pairs and Barker sequences, II, LMS Journal of Computation and Mathematics, Vol. 17, No. 1 (2014), 24-32.

B. Logan and M. J. Mossinghoff, Double Wieferich pairs and circulant Hadamard matrices, ResearchGate, 2015.

M. J. Mossinghoff, Wieferich pairs and Barker sequences, Designs, Codes and Cryptography, Vol. 53, No. 3 (2009), 149-163.

Kai-Uwe Schmidt and Jürgen Willms, Barker sequences of odd length, Des. Codes Cryptogr. Vol. 80, No. 2 (2016), 409-414.

R. Turyn and J. Storer, On binary sequences, Proceedings of the American Mathematical Society, vol. 12, no. 3, pp. 394-399, 1961.

Jürgen Willms, Counterexamples to Theorem 1 of Turyn's and Storer's paper "On Binary Sequences", arXiv:1404.4833 [math.NT], 2014.

Eric Weisstein's World of Mathematics, Barker Code

Wikipedia, Barker code.

EXAMPLE

{{+, +},  {+, -}},

{{+, +, -}},

{{+, +, +, -}, {+, +, -, +}},

{{+, +, +, -, +}},

{{+, +, +, -, -, +, -}},

{{+, +, +, -, -, -, +, -, -, +, -}},

{{+, +, +, +, +, -, -, +, +, -, +, -, +}}

CROSSREFS

Cf. A011758, A011759, A276690.

Sequence in context: A082451 A121362 A234694 * A175799 A123739 A165575

Adjacent sequences:  A091701 A091702 A091703 * A091705 A091706 A091707

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jan 30 2004

STATUS

approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)