Barker code

A Barker code or Barker sequence is a finite sequence of N values of +1 and −1,

with the ideal autocorrelation property, such that the off-peak (non-cyclic) autocorrelation coefficients

are as small as possible:

for all .

Only nine Barker sequences are known, all of length N at most 13. Barker's 1953 paper asked for sequences with the stronger condition