Dr. Francisco J. Collazo

Discrete Mathematics

Coding Theory

Math Contributors

Terr

Barker Code

This entry contributed by David Terr

A Barker code is a string of digits of length such that

for all . Barker codes are used for pulse compression of radar signals. There are Barker codes of lengths 2, 3, 4, 5, 7, 11, and 13. A complete list of Barker codes up to reversal of digits and negation is given below. The number of candidate codes of length n is therefore equal to the number of n-bead black-white reversible strings 1, 2, 3, 6, 10, 20, 36, 72, ... (Sloane's A005418), while the numbers of Barker codes of order l = 2, 3, ... are 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, and 0 for all higher n (Sloane's A091704).

length	code
2	,
3
4	,
5
7
11
13

Barker, R. H. "Group Synchronizing of Binary Digital Sequences." In Communication Theory. London: Butterworth, pp. 273-287, 1953.

Lüke, H. D. Korrelationssignale. Berlin: Springer-Verlag, 1992.

Sloane, N. J. A. Sequences A05418/M0771 and A091704 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/.

Stimson, G. W. Introduction to Airborne Radar, 2nd ed. Raleigh, NC: SciTech, p. 172, 1998.

Eric W. Weisstein et al. "Barker Code." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BarkerCode.html