  The flux-noise spectra around the Kosterlitz-Thouless transition are obtained
from simulations of the two-dimensional resistively shunted junction model. In
particular the dependence on the distance $d$ between the pick-up coil and the
sample is investigated. The typical experimental situation corresponds to the
large-$d$ limit and a simple relation valid in this limit between the complex
impedance and the noise spectra is clarified. Features, which distinguish
between the large- and small-$d$ limit, are identified and the possibility of
observing these features in experiments is discussed.
