A guess for the open problem of a complex orthogonal space-time block code for 8 transmit antennas

Recently, Xue-Bin Liang presented a new complex orthogonal space-time block code (STBC) for 8 transmit antennas, which is generated simply by padding a transmission vector for the 8th transmit antenna to the transmission matrix of the existing complex orthogonal STBC for 7. He also posed an open problem on whether or not arbitrary antennas can realize the same method. In this correspondence, we give a guess for it that if the number of antennas n = 4k - 1 (k is a natural number), then the method above is true, and the rest is not