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Everything about Complementary sequences

Pairs of sequences

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. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Complementary sequencesA 5-minute orientation
  2. Skim a recent paper: AbLang: an antibody language model for completing antibody sequencesInfluential work since 2022
  3. Pick up a classic book: cDNA preparation and characterizationThe most-reprinted book on the subject
  4. Read the landmark paper: Complementary sets of sequencesCited 527 times
  5. Go sideways: Wiener–Khinchin theoremA closely related topic
  6. Go sideways: Haar waveletA closely related topic

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