Turyn‐Type Sequences: Classification, Enumeration, and Construction
Copyright policy )Turyn‐Type Sequences: Classification, Enumeration, and Construction
AbstractTuryn‐type sequences, , are quadruples of ‐sequences , with lengths , respectively, where the sum of the nonperiodic autocorrelation functions of and twice that of is a δ‐function (i.e., vanishes everywhere except at 0). Turyn‐type sequences are known to exist for all even n not larger than 36. We introduce a definition of equivalence to construct a canonical form for in general. By using this canonical form, we enumerate the equivalence classes of for . We also construct the first example of Turyn‐type sequences .
- University of Lethbridge Canada
- University of Waterloo Canada
canonical form, nonperiodic autocorrelation functions, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Turyn-type sequences, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
canonical form, nonperiodic autocorrelation functions, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Turyn-type sequences, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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