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Barker Codes

The (ACF) Autocorrelation Function of Barker Sequences has off-peak values of 1,0 or -1. If aperiodic autocorrelation of a sequence reaches the lower bound of |ACF| = 1, it is a Barker Sequence.

The Barker Sequences which have the length 3, 4, 5, 7, 11 and 13 are only known. Considering all the binary codes, the best autocorrelation properties belong to the length-11 and length-13 Barker sequences.

Applications of Barker sequences are IEEE 802.11b WLAN (Wireless Local Area Networks)(only length-11 Barker sequence) and word synchronization in paging systems.