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
Peter Borwein and Tamas Erdelyi, A note on Barker polynomials, arXiv:1206.5371 [math.NT], 2012.
Peter Borwein and Michael J. Mossinghoff, Wieferich pairs and Barker sequences, II, LMS Journal of Computation and Mathematics, Vol. 17, No. 1 (2014), 24-32.
Shalom Eliahou, Connaît-on toutes les suites de Barker ?, Images des Mathématiques, CNRS, 2022. In French.
Luis H. Gallardo, Ryser's Conjecture and Stochastic matrices, Univ. Brest (France 2024). See p. 2.
Brooke Logan Ogrodnik and Michael J. Mossinghoff, Double Wieferich pairs and circulant Hadamard matrices, ResearchGate, 2015.
Michael 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
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jan 30 2004
STATUS
approved