In February 2014, Alexei Lisitsa and Boris Konev of the University of Liverpool showed that every sequence of 1161 or more elements satisfies the conjecture in the special case C = 2, which proves the conjecture for C ≤ 2.
Their proof relied on an SAT-solver computer algorithm whose output takes up 13 gigabytes of data, more than the entire text of Wikipedia at that time, so it cannot be independently verified by human mathematicians without further use of a computer.
[2] In September 2015, Terence Tao announced a proof of the conjecture, building on work done in 2010 during Polymath5 (a form of crowdsourcing applied to mathematics) and a suggestion made by German mathematician Uwe Stroinski on Tao's blog.
[6] This is based on the fact that in the case of finite-length sequences discrepancy is bounded.
[7] Barker codes of lengths 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties.