Rotated $D_n$-lattices in dimensions power of $3$

  • Agnaldo José Ferrari
  • Grasiele Cristiane Jorge
  • Antonio Aparecido Andrade
Keywords: Lattices, Cyclotomic fields, Signal transmission


In this work, we present constructions of families of rotated $D_n$-lattices which may be good for
signal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $\mathbb{Z} \oplus \mathcal{A}_{2}^{k}$ lattices, where $\mathcal{A}_{2}^{k}$ is a direct sum of $k=\frac{3^{r-1}-1}{2}$ copies of the $A_2$-lattice, using free $\mathbb{Z}$-modules in $\mathbb{Z}[\zeta_{3^{r}}+\zeta_{3^{r}}^{-1}]$.


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