A Simple Construction for the Barnes-Wall Lattices
<|reference_start|>A Simple Construction for the Barnes-Wall Lattices: A certain family of orthogonal groups (called "Clifford groups" by G. E. Wall) has arisen in a variety of different contexts in recent years. These groups have a simple definition as the automorphism groups of certain generalized Barnes-Wall lattices. This leads to an especially simple construction for the usual Barnes-Wall lattices. This is based on the third author's talk at the Forney-Fest, M.I.T., March 2000, which in turn is based on our paper "The Invariants of the Clifford Groups", Designs, Codes, Crypt., 24 (2001), 99--121, to which the reader is referred for further details and proofs.<|reference_end|>
@article{nebe2002a,
    title={A Simple Construction for the Barnes-Wall Lattices},
    author={G. Nebe, E.M. Rains, N.J.A. Sloane},
    journal={Codes, Graphs, and Systems: A Celebraton of the Life and Career of
  G. David Forney Jr., ed. R. E. Blahut and R. Koetter, Kluwer, 2002, pp.
  333-342},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0207186},
    primaryClass={math.CO cs.IT math.IT}
}