✦ LIBER ✦

Merit factors and Morse sequences

✍ Scribed by T. Downarowicz; Y. Lacroix

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 656 KB
Volume: 209
Category: Article
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00121-2

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✦ Synopsis

We show that Turyn's conjecture, arising from the Theory of Error Correcting Codes, has an equivalent formulation in Dynamical Systems Theory. In particular, Turyn's conjecture is true if all binary Morse flows have singular spectra. Our proof uses intermediate estimates for merit factors of products of words, and is purely combinatorial. @ 1998-Elsevier Science B.V. All rights reserved Nous montrons que la conjecture de Turyn, issue de la ThCorie des Codes Correcteurs d'Erreur, a une formulation iquivalente en ThCorie des Sys3mes Dynamiques. En particulier, la premitre est vraie si tous les flats de Morse continus binaires ont un spectre singulier. La preuve utilise des estimations interrnkdiaires du facteur de m&rite d'un produit de mats, et repose sur des mkthodes purement combinatoires.

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