be error free by auto 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” Definition 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 are as small as possible: for all . Only nine Barker sequences are known, all of length N at most 13. Barker's 1953 paper asked for sequences with the stronger condition Only four such sequences are known, shown in bold in the table below. Known Barker codes Here is a table of all known Barker codes, where negations and reversals of the codes have been omitted. A Barker code has a maximum autocorrelation sequence which has sidelobes no larger than 1. It is generally accepted that no other perfect binary phase codes exist. (It has been proven that there are no further odd-length codes, nor even-length codes of .) Barker codes of length N equal to 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties (The sidelobe level of amplitude of the Barker codes is 1/N that of the peak signal). A Barker code resembles a discrete version of a continuous chirp, another low-autocorrelation signal used in other pulse compression radars. The positive and negative amplitudes of the pulses forming the Barker codes imply the use of biphase modulation or binary phase-shift keying; that is, the change of phase in the carrier wave is 180 degrees. Similar to the Barker codes are the complementary sequences, which cancel sidelobes exactly when summed; the even-length Barker code pairs are