  In this letter, we propose a Voronoi shaping method with reduced encoding
complexity. The method works for integer shaping and coding lattices satisfying
the chain $\Lambda_s \subseteq \textbf{K}\mathbb{Z}^n \subseteq \Lambda_c$,
with $\textbf{K}$ an integer diagonal matrix. This assumption is easily
satisfied for lattices obtained from error-correcting codes. For those
lattices, using this strategy, an explicit set of coset representatives is
obtained and lattice encoding complexity is reduced to the linear code encoding
complexity. Our proposal is illustrated in construction-D lattices with Gosset
($E_8$) and Leech ($\Lambda_{24}$) lattices as shaping lattices.
