Spherical 5-designs obtained from finite unitary groups

Let G = U-2m (2) be the unitary group of dimension 2m greater than or equal to 6 over the finite field of four elements GF(4), W = GF(4)(2m) the natural module of G. Then G acts transitively on the set Omega of maximal totally isotropic m-dimensional subspaces of W. This permutation representation over R contains an irreducible representation of dimension d = (4(m) + 2)/3. One can embed the set Omega into the unit sphere Sd-1 in the Euclidean space R-d, and we prove that this embedding gives a spherical 5-design. (C) 2003 Elsevier Ltd. All rights reserved.