I have studied low-density parity-check (LDPC) codes, which use quasi-cyclic codes whose submatrices are cyclic shifts of the identity matrix or of the zero matrix. For example,
Each number means: $-1$ is all zero matrix, if not $-1$ it is shift amount.
I need mathematical theory about this kind of matrix, but I can't find any theory when I search about quasi-cyclic LDPC, cyclic matrix , circulant matrix. So, if anyone know name of this kind of matrix, please tell me.