Abstract

SEGURA UGALDE, Esteban  and  PIZA VOLIO, Eduardo. Turyn Type Sequences. Rev. Mat [online]. 2019, vol.26, n.2, pp.253-279. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v26i2.38317.

In this paper we study the so called Turyn type sequences and some heuristics algorithms to generate them. The importance of these sequences lies, at least, in the fact that they can be used to construct some Hadamard matrices of order 4(3m − 1), where m is the length of the Turyn type sequence through the theorem of Goethals-Seidal. We simplify the proof of Turyn’s theorem (see Theorem 3). In addition, we find some interesting theoretical results (see Theorem 5). Finally, we develop several efficient heuristic algorithms, comparable to the algorithms already known, that generate Turyn type sequences of sizes less than or equal to 40.

Keywords : Turyn type sequences; Goethals-Seidel theorem; Hadamard matrices; simulated annealing; combinatorial optimization.

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