New Packings in Grassmannian Space

We provide a new algebraic construction for packing subspaces in complex Grassmannian space with respect to the chordal distance metric. The proposed method extends the construction of character-polynomial (CP) subspace codes, recently proposed by the authors, to higher dimensions. Our results indicate the superiority of the packings derived from CP codes in the real Grassmannian space compared with existing explicit construction. Furthermore, we propose a concatenation method in Grassmannian space and characterize the rate and the minimum distance of a concatenated Grassmann code in terms of those of its underlying inner and outer codes. This result is then utilized to arrive at the counterpart of Zyablov bound in Grassmannian space. Finally, we construct Grassmann codes with asymptotically large blocklength simultaneously attaining non-vanishing rate and normalized minimum distance. In particular, we propose a family of concatenated Grassmann codes having CP inner codes that surpass the Zyablov bound in the low-rate regime.