On the construction of perfect codes from HEX signal constellations

► An innovative methodology for perfect codes for any channel of any dimension n is proposed. ► Minimum and non-minimum perfect codes are considered as subsets of cyclic division algebras over Q(ζ3). ► The signal constellation is isomorphic to the hexagonal A2n-rotated lattice. ► Constellation shaping and uniform energy property have been demonstrated for QAM and HEX constellations.