Turyn‐Type Sequences: Classification,Enumeration, and Construction |
| |
| Authors: | D Best D Ž Ðoković H Kharaghani H Ramp |
| |
| Institution: | 1. Department of Mathematics and Computer Science, University of Lethbridge, , Lethbridge, Alberta, T1K 3M4 Canada;2. Department of Pure Mathematics and Institute for Quantum Computing, University of Waterloo, , Waterloo, Ontario, N2L 3G1 Canada |
| |
| Abstract: | Turyn‐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  . |
| |
| Keywords: | Turyn-type sequences nonperiodic autocorrelation functions canonical form |
|
|
