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Construct syndrome table for signal bit error patterns. Using syndromes, find error pattern and codeword for each of the following received vectors.

Parity Check matrix for (7,3) code is given below.

$H = \begin{bmatrix} \ 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ \ 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ \ 1 & 1 & 0 & 0 & 0 & 1 & 0 \\ \ 1 & 1 & 1 & 0 & 0 & 0 & 1 \\ \end{bmatrix}$

Construct syndrome table for signal bit error patterns. Using syndromes, find error pattern and codeword for each of the following received vectors.

$r_1= 0011101, r_2 = 1101110$.

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