On the conjectures of SU(3) and AB unitary space-time codes

Proofs to the conjectures made by Jing and Hassibi on having fully diverse (3 × 3) SU(3) and AB unitary space-time codes are presented in this correspondence. We first prove that the SU(3) codes are fully diverse if and only if the design parameters P, Q, R, and are all odd integers, and in addition, are relatively prime. For the type I AB codes, it is shown that full diversity can be achieved if and only if the integers P, Q, R, and S are relatively prime. Finally, we show that such condition is also sufficient for having fully diverse type II AB codes.