TY - JOUR
T1 - Augmented product codes and lattices
T2 - Reed-Muller codes and Barnes-Wall lattices
AU - Salomon, Amir J.
AU - Amrani, Ofer
PY - 2005/11
Y1 - 2005/11
N2 - 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.
AB - 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.
KW - (Decomposable) binary lattice
KW - (Principal sublattices of) Barnes-Wall lattice
KW - Binary code
KW - Lattice
KW - Lattice/code (deep) holes
KW - Product code
KW - Product lattice
KW - Reed-Muller code
UR - http://www.scopus.com/inward/record.url?scp=27744603302&partnerID=8YFLogxK
U2 - 10.1109/TIT.2005.856937
DO - 10.1109/TIT.2005.856937
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AN - SCOPUS:27744603302
SN - 0018-9448
VL - 51
SP - 3918
EP - 3930
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 11
ER -