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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.

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    it doesn't just "look" like a block-Toeplitz matrix, it IS one! Simply define the two 2x1 blocks: [a;c] and [b;d]...2010-10-20

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You could call it block circulant even, which is more restrictive than Toeplitz. A block matrix does not need every block to be the same size. As Laurent wrote above: Just consider the blocks to be $2 \times 1$ matrices instead of $2 \times 2$ and you will be fine.