A Simple Construction for the Barnes-Wall Lattices

Details A Simple Construction for the Barnes-Wall Lattices A Simple Construction for the Barnes-Wall Lattices

2002-07-22

arxiv.org/abs/math/0207186v1

Codes, Graphs, and Systems: A Celebraton of the Life and Career of G. David Forney Jr., ed. R. E. Blahut and R. Koetter, Kluwe

Mathematics

Combinatorics

10 pp., 2 figs.; To Dave Forney, on the occasion of his sixtieth birthday

Scientific paper

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.

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