A Simple Construction for the Barnes-Wall Lattices
Combinatorics
2007-07-16 v1 Information Theory
math.IT
Abstract
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.
Cite
@article{arxiv.math/0207186,
title = {A Simple Construction for the Barnes-Wall Lattices},
author = {G. Nebe and E. M. Rains and N. J. A. Sloane},
journal= {arXiv preprint arXiv:math/0207186},
year = {2007}
}
Comments
10 pp., 2 figs.; To Dave Forney, on the occasion of his sixtieth birthday