Question

Q.3 (a) For a (6, 3) systematic linear block code, the three parity check bits are formed from the following equations: b? = m? + m? + m? b? = m? + m? b? = m? + m? (a) Write down the generator matrix $\tilde{G}$ (b) Construct all possible code-words. (b) Consider a (7, 4) linear block code whose generator matrix is given by: $\begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 & 0\\1 & 1 & 1 & 0 & 1 & 0 & 0\\1 & 1 & 0 & 0 & 0 & 1 & 0\\0 & 1 & 1 & 0 & 0 & 0 & 1 \end{bmatrix}$ (a) Find all the code vectors of this code. (b) Find the minimum distance of this code.

          Q.3
(a) For a (6, 3) systematic linear block code, the three parity check bits are formed from
the following equations:
b? = m? + m? + m?
b? = m? + m?
b? = m? + m?
(a) Write down the generator matrix $\tilde{G}$
(b) Construct all possible code-words.
(b) Consider a (7, 4) linear block code whose generator matrix is given by:
$\begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 0 & 0\\1 & 1 & 1 & 0 & 1 & 0 & 0\\1 & 1 & 0 & 0 & 0 & 1 & 0\\0 & 1 & 1 & 0 & 0 & 0 & 1 \end{bmatrix}$
(a) Find all the code vectors of this code.
(b) Find the minimum distance of this code.

Q.3
(a) For a (6, 3) systematic linear block code, the three parity check bits are formed from
the following equations:
b? = m? + m? + m?
b? = m? + m?
b? = m? + m?
(a) Write down the generator matrix G̃
(b) Construct all possible code-words.
(b) Consider a (7, 4) linear block code whose generator matrix is given by:
< b m a t r i x >
(a) Find all the code vectors of this code.
(b) Find the minimum distance of this code.

Added by Paul K.

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