Augmented Product Codes and Lattices: Reed–Muller Codes and Barnes–Wall Lattices
Amir J. Salomon, Ofer Amrani · IEEE Transactions on Information Theory · 2005
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 higher dimensional codes or lattices from the same class, respectively. Certain properties of the augmented product construction are derived, and specific construction examples are given. 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 various augmented product constructions.