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Turyn-Type Sequences: Classification, Enumeration, and Construction



Turyn-type sequences, math formula, are quadruples of math formula-sequences math formula, with lengths math formula, respectively, where the sum of the nonperiodic autocorrelation functions of math formula and twice that of math formula is a δ-function (i.e., vanishes everywhere except at 0). Turyn-type sequences math formula are known to exist for all even n not larger than 36. We introduce a definition of equivalence to construct a canonical form for math formula in general. By using this canonical form, we enumerate the equivalence classes of math formula for math formula. We also construct the first example of Turyn-type sequences math formula.