Secuencias tipo Turyn

• SEGURA UGALDE, ESTEBAN ^[1] ; PIZA VOLIO, EDUARDO ^[1]
  1. [1] Universidad de Costa Rica

     Universidad de Costa Rica

     Hospital, Costa Rica

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 26, Nº. 2, 2019 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 253-279
• Idioma: español
• DOI: 10.15517/rmta.v26i2.38317
• Títulos paralelos:
  • Turyn type sequences
• Enlaces
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• Resumen
  • español

    En este artículo estudiamos fundamentalmente las denominadas secuencias tipo Turyn y algunos algoritmos heurísticos para generarlas. La importancia de estas secuencias estriba, al menos, en el hecho de quepueden ser empleadas en la construcción de algunas matrices de Hadamard de órdenes 4(3m - 1), donde m es el largo de la secuencia tipo Turyn a través del uso del teorema de Goethals-Seidal. Simplificamos la demostración del teorema de Turyn (ver Teorema 3). Además, hallamos algunos resultados teóricos interesantes (ver Teorema 5). Finalmente, desarrollamos varios algoritmos heurísticos eficientes, comparables a los algoritmos ya conocidos, que generan secuencias tipo Turyn de tamañosmenores o iguales a 40.

  • English

    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.

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