The tenth realization is based on a publication of Forney [7]. He describes generalized state realizations for Reed-Muller codes that are built by 2 x 2 Hadamard transform blocks:
Such a block implements
s = a0 = A0
s + a1 + A1 = 0.
Note that the [8,4,4] first-order Reed-Muller code is equivalent to the [8,4,4] extended Hamming code. Therefore, the [8,4,4] extended Hamming code also can be described by such blocks:
The realization looks then as follows:
