Barker code

A Barker code is a sequence of N values of +1 and -1,

a_j for j = 0,1,...,N − 1,

such that

|Σ_j=0^N-v a_j a_j+v| <= 1

for all 1 <= v < N.

Here is a table of all known Barker codes, where negations and reversals of the codes have been omitted:

Known Barker Codes

Length	Codes
2	+1 −1	+1 +1
3	+1 +1 −1
4	+1 −1 +1 +1	+1 −1 −1 −1
5	+1 +1 +1 −1 +1
7	+1 +1 +1 −1 −1 +1 −1
11	+1 +1 +1 −1 −1 −1 +1 −1 −1 +1 −1
13	+1 +1 +1 +1 +1 −1 −1 +1 +1 −1 +1 −1 +1

Barker codes of length 11 and 13 are used in direct-sequence spread spectrum systems because of their low autocorrelation properties.

References

• Barker Code — Mathworld
• COM-1012 DIRECT SEQUENCE SPREAD-SPECTRUM MODULATOR