A Simple Construction for the Barnes-Wall Lattices

G. Nebe; E. M. Rains; N. J. A. Sloane

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A Simple Construction for the Barnes-Wall Lattices

G. Nebe·E. M. Rains·N. J. A. Sloane

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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.

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BibTeX RIS

G. Nebe, E. M. Rains, N. J. A. Sloane. 2002-07-22. A Simple Construction for the Barnes-Wall Lattices. https://arxiv.org/abs/math/0207186

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