Spherical 5-designs obtained from finite unitary groups

  • Authors:

  • Akihiro Munemasa

  • Affiliations:

  • Division of Mathematics, Graduate School of Information Sciences, Tohoku University, 09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan and Department of Mathematics, Kyushu University, Fukuoka ...

  • Venue:
  • European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let G = U2m (2) be the unitary group of dimension 2m ≥ 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 Ω of maximal totally isotropic m-dimensional subspaces of W. This permutation representation over R contains an irreducible representation of dimension d = (4m + 2)/3. One can embed the set Ω into the unit sphere Sd-1 in the Euclidean space Rd, and we prove that this embedding gives a spherical 5-design.