Word Count : 549

---

We are asked to find the parity-check matrix (\overline{\mathcal{H}}_3) and decode several vectors. Let’s solve it manually step by step. --- Assume (\overline{\mathcal{H}}_3) corresponds to a standard ((8,4)) Hamming code (since vectors are length 8), then the parity-check matrix is formed from all non-zero 3-bit binary columns: [ \overline{\mathcal{H}}_3 = \begin{bmatrix} 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \ 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \end{bmatrix}. ] But to make it easier, let's denote Hamming (8,4) _______ __________ _________ _______ ______.
_________ ________ ____ ____ ____ _________ _____ ____ _________.
_______ _________ ______ ____ ____ _____ _____ ____.
______ _____ _________ __________ ______ ______ ___ _______.
_______ _________ ___ __________ ______ ______ _____ _______ __________ ______ ________.
________ ________ ____ ____ _________ ____ __________ ________ ________ _______.
____ ____ ___ ________ ___ ___ ______.
_____ _______ __________ _____ _______ _________ __________ _________ ______.
________ _______ ______ ___ ____ __________ _______.
__________ ____ _________ ___ _____ _______ ________ ______.
___ _________ ___ ______ ________ __________ _______ ______ _______.
______ _____ _______ ______ ____ _________ _______ _____ ____ ___.
_______ ___ ________ _________ __________ _____ ____ _________ ___ ___ _______.
_______ ______ _________ __________ ___ _______ _______.
____ ___ ___ ________ ___ ______ ______ _______ __________ _________ ___ __________.
_______ __________ _______ __________ ________.
__________ _________ _______ ____ __________.
____ __________ ____ __________ ________ _____ ___.
_________ __________ ___ ______ ________ ______.
____ ____ __________ _________ _______ __________ ______ _______ _____ ________.
____ _____ _________ ____ _____ _______ _________.
_________ _______ ________ __________ ________ ______ ________ _______ ________.
__________ ___ __________ ________ ______ ______ _________ ______ ___ _______ _______.
_______ ______ ___ ____ _________ __________ ________.
______ _________ _________ __________ ______ _______ _______ _____ ___ _____ _______ _______.
_______ _______ _____ ___ ________ _______ __________ ____.
_____ __________ ________ ____ ______ ______ __________ _____ ______ ____ _______.
___ ________ _________ _____ _______ ______ ________ ___.
__________ _____ _______ ____ _______ ______ ________.
___ __________ _______ ________ ___ ______ ______ __________.
__________ ________ ________ ____ ____ ______ _____ _____ _________ _______.
______ ___ _______ ____ ________ ___.
___ ______ ____ ______ ___ __________ ________ __________ ___ __________.
_________ _________ __________ _________ ____ _______ _________ ____.
____ ________ _____ ____ ________ _____.
__________ ____ ____ __________ _____ _____ _______ __________.
__________ ____ ___ ____ _____ ______ _________ __________.
_______ ________ ___ ______ _______ __________ ______ ____ _________.
_________ ___ ____ ____ ______ ___ ___ ____ ___ __________ ___.
________ ________ _________ _____ _____ _______ ___ ____ ___ __________ ________ _____.
__________ ______ ________ ______ _______ ____ __________ ______ _______.
_______ ________ _________ _____ ______ ___ ___.
_____ _____ __________ ________ _________ _____ ____ ____.
__________ ___ _______ _______ _____ ____ _______.
________ ________ ________ ___ ______ ________ ___ ___.
_______ _________ __________ _____ _______.
_________ __________ _____ ____ _________ _____ __________ _____ ________ __________ _________ _______.
________ _________ ______ _______ __________ ___ ________.
________ _________ ___ ______ ____ _______ _____ _____ ________ __________ _________ ___.
____ ______ ___ _____ ______ ____ ___ _____ __________.
__________ _________ _________ _______ _________ ____ _____ ____.
______ ______ _____ ______ ____ ____ __________.
____.
Get Full Answer on WhatsApp