Plain English explanation of the Space-time Code Block by Alamouti
I suppose I am safe to assume you are referring to this.

It is a method used to transmit data reliably across difficult environments. The idea is to transmit the same block of data, many times across space and time. transmitting many copies across time means, well, to transmit the same data many and at different times. Transmitting them across space means, well, to transmit them from many different points in space using different antennas. Than all these transmissions are re-combined to reconstruct the original signal.

One of the ways to reconstruct the original signal is to first build a linear algebra-based model of the system. $$Y = H X + N$$

where: Y is the output matrix (the signals received across time and space), X is the input matrix (the signals transmitted across space), H is a matrix that represents the code, and N is noise.

If the signals were transmitted only across space (only one time) then H would be a square matrix with each element \$h_{ij}\$ representing the gain from antenna \$i\$ to antenna \$j\$. However, the signals are transmitted across time and with other changes applied to them. Hence, the elements of matrix \$H\$ will have such values to reflect those transformations.

The idea is to find the inverse of H or most commonly the pseudo-inverse of H since it might not be square. After doing so (there are plenty of methods to do so), the transmitted signal can be computed as follows.

$$\hat{X} = H^+ Y$$

where: \$\hat{X}\$ is the estimation of the original signal across time and \$H^+\$ is the pseudo-inverse of \$H\$. The error would be \$H^+ N\$.

The values of \$\hat{H}\$ are finally combined to get a good estimate of the original block of data. This is usually done by just looking at the the minimum distance of the signal values from the symbols used to transmit the data.