In this paper equation 11, the author uses a symbol that is a cross in a circle. I believe I have seen that referred to as a direct sum, but I am not completely sure what that is.
This is an example of, what I call, a two-pass paragraph (I try to avoid these when writing). It's a situation in which you need to keep reading to understand the previous material.
If you keep reading, you'll find:
So $\phi(y)$ is the $4 \times 4$ diagonal matrix with the diagonal entries as listed in (11).