Augmented product codes and lattices: Reed-Muller codes and Barnes-Wall 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 higher dimensional codes or lattices from the same class, respectively. Certain propert...

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Veröffentlicht in:	IEEE transactions on information theory 2005-11, Vol.51 (11), p.3918-3930
Hauptverfasser:	Salomon, A.J., Amrani, O.
Format:	Artikel
Sprache:	eng
Schlagworte:	(decomposable) binary lattice (principal sublattices of) Barnes-Wall lattice Applied sciences Binary code Binary codes Codes Coding, codes Communication channels Construction Construction specifications Decoding Exact sciences and technology Golay codes Information theory Information, signal and communications theory lattice Lattice theory lattice/code (deep) holes Lattices Leeches product code Product codes product lattice Random access memory Reed-Muller code Signal and communications theory Telecommunications and information theory
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Beschreibung
Zusammenfassung:	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.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2005.856937