Around Pelikan's conjecture on very odd sequences

Details Around Pelikan's conjecture on very odd sequences Around Pelikan's conjecture on very odd sequences

2004-07-06

arxiv.org/abs/math/0407084v2

Manuscripta Mathematica 117 (2005), 219-238

Mathematics

Number Theory

21 pages, two tables. Revised version with improved presentation and correction of some typos and minor errors that will appea

Scientific paper

10.1007/s00229-005-0554-5

Very odd sequences were introduced in 1973 by J. Pelikan who conjectured that there were none of length >=5. This conjecture was disproved by MacWilliams and Odlyzko in 1977 who proved there are in fact many very odd sequences. We give connections of these sequences with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on their lengths and on S(n), which denotes the number of very odd sequences of length n.

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