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, and it is conjectured that no longer Barker
codes exist. A list of known Barker codes up to reversal of digits and negation is
given below.
length
code
2
,
3
4
,
5
7
11
13
The number of candidate codes of length is therefore equal to the number of -bead black-white reversible strings 1, 2, 3, 6, 10, 20, 36,
72, ... (OEIS A005418), while the numbers of
Barker codes of order ,
3, ... are 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, and 0 for all higher (OEIS A091704).
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."Stimson,
G. W. Introduction
to Airborne Radar, 2nd ed. Raleigh, NC: SciTech, p. 172, 1998.Zwillinger,
D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 223,
1995.
of length 
such that
.
Barker codes are used for pulse compression of radar signals. There are Barker codes
of lengths 2, 3, 4, 5, 7, 11, and 13, and it is conjectured that no longer Barker
codes exist. A list of known Barker codes up to reversal of digits and negation is
given below.
, 
, 
is therefore equal to the number of 
-bead black-white reversible strings 1, 2, 3, 6, 10, 20, 36,
72, ... (OEIS A005418), while the numbers of
Barker codes of order 
,
3, ... are 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, and 0 for all higher 
(OEIS A091704).
