A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
Designs, Codes and Cryptography
Bounds for codes and designs in complex subspaces
Journal of Algebraic Combinatorics: An International Journal
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We introduce the notion of a it-design on the Grassmann manifold \cal Gim,n of the im-subspaces of the Euclidean space \Bbb Rin. It generalizes the notion of antipodal spherical design which was introduced by P. Delsarte, J.-M. Goethals and J.-J. Seidel. We characterize the finite subgroups of the orthogonal group which have the property that all its orbits are it-designs. Generalizing a result due to B. Venkov, we prove that, if the minimal im-sections of a lattice iL form a i4-design, then iL is a local maximum for the Rankin function γin,m.