Voronoi Constellations of Generalized Construction D’ Lattices from q-ary Codes

In this paper, we present a scheme for obtaining Voronoi constellations of Generalized Construction D’ lattice obtained from q-ary codes. For this, we first extend the Generalized Construction D’ to a chain of linear q-ary codes, establish a connection with Construction A and derive a generator matrix, expressions for the minimum distance and the volume of this lattice. This connection also allowed to extend an efficient previous scheme for obtaining Voronoi constellations of Construction A to Generalized Construction D’ lattices.