Abstract—The maximal rates and the minimal delays are basic problems of space-time block codes from complex orthogonal designs. Liang systematically solved the problem on the maximal rates of complex othogonal designs, and posed an open problem on the minimal delays. Recently, the authors gave the negative answer for the open problem. In this letter, we give lower bounds on the minimal delays.

It was conjectured by Koetter and Vardy that if the characteristic generators of a linear code are linearly independent,then the corresponding characteristic generators of the dual code are also linearly independent. In this correspondence,we prove that the conjecture is true for self-dual codes and cyclic codes.

X. Liang systematically investigatedorthogonal 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 = 8and prove that the minimal delay for complex orthogonal designs with eight columns is 56. Hence, we give a negative answer for the open problem.