Ferrari, Agnaldo José [UNESP]De Andrade, Antonio Aparecido [UNESP]2018-12-112018-12-112018-09-01Journal of Algebra and its Applications, v. 17, n. 9, 2018.0219-4988http://hdl.handle.net/11449/170217In this paper, we present the constructions of rotated ℤ3r-1-lattices, where r is a positive integer, via ℤ-modules of the ring of the integers ℤ [ζ3r+ζ 3r-1]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. Lower bounds for the minimum product distances of such construction are also presented.engCyclotomic fieldideal latticeminimum product distancerotated latticeArtigo10.1142/S021949881850175XAcesso restrito2-s2.0-85030330619