A variant of the Johnson–Lindenstrauss lemma for circulant matrices

We continue our study of the Johnson–Lindenstrauss lemma and its connection to circulant matrices started in Hinrichs and Vybíral (in press) [7], . We reduce the bound on k from k=Ω(ε−2log3n) proven there to k=Ω(ε−2log2n). Our technique differs essentially from the one used in Hinrichs and Vybíral (in press) [7]. We employ the discrete Fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure.