**Problem 8: Binary Linear Block Code**Consider the (6,3) binary linear block code defined by the following generator matrix:\[ G = \begin{bmatrix} 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 \end{bmatrix} \]**Tasks:**(a) Find the parity-check matrix \( H \).(b) Assume that the correctible error patterns are all 1-bit error patterns and a 2-bit error pattern \( 010001 \). Decode the received vector \( \mathbf{r} = (111101) \).

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Answered: Consider the (6,3) binary linear block…

Consider the (6,3) binary linear block code defined by the following generator matrix: 1 1 1 G = 1 1 1 1 1 1. Eind the narity-check matrix H.

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Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

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Question

**Problem 8: Binary Linear Block Code**

Consider the (6,3) binary linear block code defined by the following generator matrix:

\[
G = \begin{bmatrix}
0 & 1 & 1 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 & 0 \\
1 & 1 & 0 & 0 & 0 & 1
\end{bmatrix}
\]

**Tasks:**

(a) Find the parity-check matrix \( H \).

(b) Assume that the correctible error patterns are all 1-bit error patterns and a 2-bit error pattern \( 010001 \). Decode the received vector \( \mathbf{r} = (111101) \).

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