  We prove a variant of a Johnson-Lindenstrauss lemma for matrices with
circulant structure. This approach allows to minimise the randomness used, is
easy to implement and provides good running times. The price to be paid is the
higher dimension of the target space $k=O(\epsilon^{-2}\log^3n)$ instead of the
classical bound $k=O(\epsilon^{-2}\log n)$.
