Trinca Watanabe, C. C.Belfiore, J. C.De Carvalho, E. D. [UNESP]Vieira Filho, J. [UNESP]2022-04-282022-04-282018-01-01International Journal of Applied Mathematics, v. 31, n. 1, p. 63-72, 2018.1314-80601311-1728http://hdl.handle.net/11449/221020Lattices can be applied in different areas of research, particularly, they can be applied in information theory and encryption schemes. Signal constellations having lattice structure have been used as a support for signal transmission over the Gaussian and Rayleigh fading channels. The problem to find a good signal constellation for Gaussian channels is associated to the search of lattices which present a good packing density, that is, dense lattices. In this way, we propose an algebraic framework to construct the dense lattice E8 from the principal ideal I = ((1 + ξ3) + ξ3ξ24 + ξ3ξ24 2) of the cyclotomic field Q(ξ24), where ξ3 and ξ24 are the third and 24-th root of unity, respectively. The advantage of obtaining lattices from this method is the identification of the lattice points with the elements of a number field. Consequently, it is possible to utilize some properties of number fields in the study of such lattices.63-72engCyclotomic fieldDense latticeE8-latticePrincipal idealArtigo10.12732/ijam.v31i1.62-s2.0-85042432002