[8,4,4] Ext. Hamming Code: Realization 2

We introduce four hidden states:

s2 = u0 + u1
s3 = u1 + u2
s0 = u2 + u3
s1 = u3 + u0.

When considering the parity-check matrix

|   1 1 1 0   1 0 0 0   |

H = |   1 1 0 1   0 1 0 0   |

|   1 0 1 1   0 0 1 0   |

|   0 1 1 1   0 0 0 1   |

we see that the parity-check equations can be written as follows

x4 = u2 + s2
x5 = u1 + s1
x6 = u0 + s0
x7 = u3 + s3.

This yields the following realization:

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