Turyn-type sequences: Classification, Enumeration and Construction

Understand

Turyn-type sequences, TT(n), are quadruples of {+,-1}-sequences (A;B;C;D), with lengths n,n,n,n-1 respectively, where the sum of the nonperiodic autocorrelation functions of A,B and twice that of C,D is a delta-function (i.e., vanishes everywhere except at 0).

• Turyn-type sequences TT(n) are known to exist for all even n not larger than 36.
• We introduce a definition of equivalence to construct a canonical form for TT(n) in general.
• By using this canonical form, we enumerate the equivalence classes of TT(n) for n up to and including 32.