Based on algebraic number theory we construct some families of rotated D n -lattices with full diversity which can be good for signal transmission over both Gaussian and Rayleigh fading channels. Closed-form expressions for the minimum product distance of those lattices are obtained through algebraic properties.
The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are not ideals in subfields of cyclotomic fields. The focus is on totally real number fields and the associated full diversity lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. We also discuss on the existence of a number field K such that it is possible to obtain the lattices A 2 , E 6 and E 7 via a twisted embedding applied to a fractional ideal of O K .
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