On the existence of rotated $D_n$-lattices constructed via Galois   extensions
  In this paper we construct families of rotated $D_n$-lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels via subfields of cyclotomic fields. These constructions exhibit full diversity and good minimum product distance which are important parameters related to the signal transmission error probability. It is also shown that for some Galois extensions $\matK|\matQ$ it is impossible to construct rotated $D_n$-lattices via fractional ideals of $\mathcal O_{\mattK}$. 
Grasiele Cristiane Jorge and Sueli Irene Rodrigues Costa
math.NT