Embed the generalized quadrangle spherical code family into Stiefel manifolds

Ascertain whether the spherical codes arising from the generalized quadrangle family can be embedded into a Stiefel manifold StF(d,r) (over R or C) with chordal distance so that they are realized as Stiefel codes.

Background

The paper recalls four known infinite families of optimal spherical codes and shows that three of these can be realized as optimal Stiefel codes. The remaining family arises from generalized quadrangles, with parameters described in the spherical coding literature.

The authors ask whether this generalized quadrangle family can be mapped into the Stiefel setting, thereby extending the repertoire of spherical-to-Stiefel embeddings of optimal codes.