  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.
