What is the name of the following matrix?
$$\begin{pmatrix} a & b & 0 \\ c & d & 0 \\ 0 & a & b\\ 0& c& d& \\ b & 0 & a \\ d & 0 & c\end{pmatrix}$$
It looks like a Block Toeplitz matrix, but usually one defines those by full shifts by (in this case) $2 \times 2$ matrices. In particular, I'm interested in solving linear equations of this form. Any reference would be appreciated.