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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〔https://oeis.org/A091704〕 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.〔http://www.math.wpi.edu/MPI2008/TSC/TSC-MPI.pdf〕 (It has been proven that there are no further odd-length codes,〔Turyn and Storer, "On binary sequences", Proceedings of the AMS, volume 12 (1961), pages 394–399〕 nor even-length codes of ''N'' < 1022.〔Leung, K., and Schmidt, B., "The Field descent method", Design, Codes and Cryptography, volume 36, pages 171–188〕) 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).〔Introduction to Radar Systems, 3rd Edition, Merrill I. Skolnik, McGraw–Hill, 2001〕 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 also complementary pairs. There is a simple constructive method to create arbitrarily long complementary sequences. For the case of cyclic autocorrelation, other sequences have the same property of having perfect (and uniform) sidelobes, such as prime-length Legendre sequences and maximum length sequences (MLS). Arbitrarily long cyclic sequences can be constructed. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Barker code」の詳細全文を読む スポンサード リンク
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