The Invariants of the Clifford Groups

The automorphism group of the Barnes-Wall lattice Lm in dimension 2m (m = 3) is a subgroup of index 2 in a certain "Clifford group" Cm of structure 21+2m + .O+ (2m, 2). This group and its complex analogue Xm of structure (21+2m + YZ8).Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge's 1996 result that the space of invariants for Cm of degree 2k is spanned by the complete weight enumerators of the codes C 2m , where

• Type: Conference
• Year: 2001
• Where: DCC
• Authors: Gabriele Nebe, Eric M. Rains, Neil J. A. Sloane
• Keywords: Barnes-wall Lattice Lm, Complete Weight Enumerators, Complex Analogue Xm, Computer Graphics, DCC 2001