Augmented product codes and lattices

This paper concerns the construction of the so-called augmented product codes and augmented product lattices. These are obtained by augmenting product codes or product lattices from certain classes thus obtaining a higher dimensional code or a lattice from the same class. Certain properties of the augmented product construction are derived, and a few examples are given for code/lattice constructions. In particular, it is shown that the Reed-Muller codes, the Golay code, the Barnes-Wall lattices as well as the Leech lattice all have an augmented product construction