A counterexample for the open problem on the minimal delays of orthogonal designs with maximal rates

X. Liang systematically investigated orthogonal designs with maximal rates, gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates. He also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates, and proved that the problem is correct for less than or equal to six transmit antennas. In this correspondence, we give a counterexample for the open problem for n = 8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56. Hence, we give a negative answer for the open problem.