Constructions of Grassmannian Simplices

Jean Creignou (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this article an explicit method (relying on representation theory) to construct packings in Grassmannian space is presented. Infinite families of configurations having only one non-trivial set of principal angles are found using 2-transitive groups. These packings are proved to reach the simplex bound and are therefore optimal w.r.t. the chordal distance. The construction is illustrated by an example on the symmetric group. Then some natural extends and consequences of this situation are given.

Mots clés: Explicit construction; Grassmannian packing; Space-time coding; Simplex bound; Wireless communication

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Jean Creignou. Constructions of Grassmannian Simplices. 2008. ⟨hal-00135498v4⟩