Some 2 × 2 unitary space-time codes from sphere packing theory with optimal diversity product of code size 6

In this correspondence, we propose some new designs of 2 × 2 unitary space-time codes of sizes 6, 32, 48, 64 with best-known diversity products (or product distances) by partially using sphere packing theory. In particular, we present an optimal 2 × 2 unitary space-time code of size 6 in the sense that it reaches the maximal possible diversity product for 2 × 2 unitary space-time codes of size 6. The construction and the optimality of the code of size 6 provide the precise value of the maximal diversity product of a 2 × 2 unitary space-time code of size 6.