Search for ultraflat polynomials with plus and minus one coefficients
نویسنده
چکیده
It is not known whether there exist polynomials with plus and minus one coefficients that are almost constant on the unit circle (called ultraflat). Extensive computations described in this paper strongly suggest such polynomials do not exist, and lead to conjectures about the precise degree to which flatness can be approached according to various criteria. The evidence shows surprisingly rapid convergence to limiting behavior. Connections to problems about the Golay merit factor, Barker sequences, Golay-Rudin-Shapiro polynomials, and others are discussed.
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