In applied mathematics, complementary sequences (CS) are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for constructing sequences of length 2N and gave examples of complementary sequences of lengths 10 and 26. In 1974 R. J. Turyn gave a method for constructing sequences of length mn from sequences of lengths m and n which allows the construction of sequences of any length of the form 2N10K26M.
Later the theory of complementary sequences was generalized by other authors to polyphase complementary sequences, multilevel complementary sequences, and arbitrary complex complementary sequences. Complementary sets have also been considered; these can contain more than two sequences.
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... cells, where RNA must exit the nucleus before translation starts.) The attenuator sequence, which is located between the mRNA leader sequence (5' UTR) and trp operon gene sequence ... The attenuator sequence at domain 1 contains instruction for peptide synthesis that requires tryptophans ... permit ribosomes to translate the attenuator sequence domains 1 and 2, allowing domains 3 and 4 to form a hairpin structure, which results in termination of transcription of the trp operon ...