Golay-Littlewood Problem

Identifying binary sequences {} whose autocorrelations {} are jointly as small as possible, for fixed , is important for engineering design purposes. The “best” sequences are those with the largest merit factor  . As an example, the sequence 1−1 1−1 1 1−1−1 1 1 1 1 1 has the largest  value 16912 = 140833 among all such with  = 12. As another example, the sequence 1−1 1 1−1 1 1 1−1−1−1 has the largest  value 12110 = 121 among all such with  = 10. No other merit factor exceeding 10 is known for any ; a proof that 16912 and 12110 are the maximum possible values for  is still open.