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A 'Barker code' is a sequence of N values of +1 and −1,
:$a\_j$ for $j\; =\; 1,\; cdotcdotcdot,\; N$
such that
:$|sum\_\{j=1\}^\{N-v\}\; a\_j\; a\_\{j+v\}|\; le\; 1,$
for all .
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 and Pulse Compression Radar systems because of their low autocorrelation properties.
Barker codes utilize biphase modulation; that is, the change of phase in the carrier wave is 180 degrees.

Contents

See also

References

See also

★ Pseudorandom number sequence

References

★ Barker Code — Mathworld