In telecommunication technology, a Barker code or Barker sequence is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender and receiver of a stream of bits.

Binary digits have very little meaning unless the significance of the individual digits is known. The transmission of a pre-arranged synchronising pattern of digits can enable a signal to be regenerated by a receiver with a low probability of error. In simple terms it is equivalent to tying a label to one digit after which others may be related by counting. This is achieved by transmitting a special pattern of digits which is unambiguously recognised by the receiver. The longer the pattern the more accurately the data can be synchronised and errors due to distortion omitted. These patterns are called Barker sequences or Barker codes, after the inventor Ronald Hugh Barker. The process is described in "Group Synchronisation of Binary Digital Systems" published in 1953. These sequences were initially developed for radar, telemetry, and digital speech encryption in the 1940s and 1950s.

During and after WWII digital technology became a key subject for research e.g. for radar, missile and gun fire control and encryption. In the 1950s scientists were trying various methods around the world to reduce errors in transmissions using code and to synchronise the received data. The problem being transmission noise, time delay and accuracy of received data. In 1948 the mathematician Claude Shannon published an article '"A Mathematical Theory of Communication"' which laid out the basic elements of communication. In it he discusses the problems of noise.

Shannon realised that “communication signals must be treated in isolation from the meaning of the messages that they transmit” and laid down the theoretical foundations for digital circuits. “The problem of communication was primarily viewed as a deterministic signal-reconstruction problem: how to transform a received signal, distorted by the physical medium, to reconstruct the original as accurately as possible” or see original. In 1948 electronics was advancing fast but the problem of receiving accurate data had not. This is demonstrated in an article on Frequency Shift Keying published by Wireless World.

In 1953 R. H. Barker published a paper demonstrating how this problem to synchronise the data in transmissions could be overcome. The process is described in “Group Synchronisation of Binary Digital Systems”. When used in data transmissions the receiver can read and if necessary correct the data to be error free by autocorrelation and cross correlation by achieving zero autocorrelation except at the incidence position using specific codes. The Barker sequence process at the time produced great interest, particularly in the United States as his method solved the problem, initiating a huge leap forward in telecommunications. The process has remained at the forefront of radar, data transmission and telemetry and is now a very well known industry standard, still being researched in many technology fields.

“In a pioneering examination of group synchronization of binary digital systems, Barker reasoned it would be desirable to start with an autocorrelation function having very low sidelobes. The governing code pattern, he insisted, could be unambiguously recognized by the detector. To assure this premise, Barker contended the selected pattern should be sufficiently unlikely to occur by chance, in a random series of noise generated bits”

A Barker code or Barker sequence is a finite sequence of N values of +1 and −1,

with the ideal autocorrelation property, such that the off-peak (non-cyclic) autocorrelation coefficients