Augmented product codes and lattices: Reed-Muller codes and Barnes-Wall lattices

Amir J. Salomon*, Ofer Amrani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3918-3930
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2005


  • (Decomposable) binary lattice
  • (Principal sublattices of) Barnes-Wall lattice
  • Binary code
  • Lattice
  • Lattice/code (deep) holes
  • Product code
  • Product lattice
  • Reed-Muller code

Cite this