Abstract
Let G= U 2 m (2) be the unitary group of dimension 2 m≥6 over the finite field of four elements GF(4), W= GF(4) 2 m the natural module of G. Then G acts transitively on the set Ω 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 Ω into the unit sphere S d−1 in the Euclidean space R d , and we prove that this embedding gives a spherical 5-design.
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