Around Pelikan's conjecture on very odd sequences
Number Theory
2007-05-23 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0407084,
title = {Around Pelikan's conjecture on very odd sequences},
author = {Pieter Moree and Patrick Sole},
journal= {arXiv preprint arXiv:math/0407084},
year = {2007}
}
Comments
21 pages, two tables. Revised version with improved presentation and correction of some typos and minor errors that will appear in Manuscripta Mathematica