Grassmannian packings from orbits of projective group representations
Renaud-Alexandre Pitaval, Olav Tirkkonen · 2012
We discuss group orbits to construct codes in the complex Grassmann manifold. Finite subgroups of the unitary group act naturally on the Grassmann manifold. Given an irreducible representation of the group of the appropriate degree, its center has no effect in orbit construction. Thus, to generate Grassmann orbit codes, projective unitary representations of finite groups are of specific interest. Following this principle, we derive basic properties and describe explicit constructions of group orbits leading to some optimum packings in 2 and 4 dimensions.