Turyn-type sequences: Classification, Enumeration and Construction
Combinatorics
2013-01-22 v1
Abstract
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. We also construct the first example of Turyn-type sequences TT(38).
Cite
@article{arxiv.1206.4107,
title = {Turyn-type sequences: Classification, Enumeration and Construction},
author = {D. Best and D. Z. Djokovic and H. Kharaghani and H. Ramp},
journal= {arXiv preprint arXiv:1206.4107},
year = {2013}
}
Comments
14 pages, 3 tables