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Around Pelikán’s conjecture on very odd sequences

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Abstract

Very odd sequences were introduced in 1973 by Pelikán who conjectured that there were none of length ≥ 5. This conjecture was disproved first by MacWilliams and Odlyzko [17] in 1977 and then by two different sets of authors in 1992 [1], 1995 [9]. We give connections with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on the length of very odd sequences and the number of such sequences of a given length.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Pieter Moree

  2. CNRS-I3S,ESSI, Route des Colles, 06903, Sophia Antipolis, France

    Patrick Solé

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  1. Pieter Moree
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  2. Patrick Solé
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Correspondence to Pieter Moree.

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Moree, P., Solé, P. Around Pelikán’s conjecture on very odd sequences. manuscripta math. 117, 219–238 (2005). https://doi.org/10.1007/s00229-005-0554-5

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  • DOI: https://doi.org/10.1007/s00229-005-0554-5

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