Title :
Augmented product codes and lattices: Reed-Muller codes and Barnes-Wall lattices
Author :
Salomon, Amir J. ; Amrani, Ofer
Author_Institution :
Dept. of Electr. Eng.-Syst., Tel-Aviv Univ., Israel
Abstract :
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.
Keywords :
Golay codes; Reed-Muller codes; binary codes; product codes; Barnes-Wall lattices; Golay code; Leech lattice; Reed-Muller code; augmented product code construction; binary code; Binary codes; Decoding; Lattices; Product codes; Random access memory; (decomposable) binary lattice; (principal sublattices of) Barnes-Wall lattice; Binary code; Reed-Muller code; lattice; lattice/code (deep) holes; product code; product lattice;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.856937