Question

The party-check matrix of a (6,3) linear block code is given by,

$H=\left[\begin{array}{cccccc}1& 0& 0& 1& 0& 1\\ 0& 1& 0& 1& 1& 0\\ 0& 0& 1& 0& 1& 1\end{array}\right]$

If the code word received by the receiver is [001110], then the syndrome vector corresponding to the received code word will be equal to

• A. [101]
• B. [100]
• C. [000]
• D. [110]

Answer 1

The correct option is B [100]

If the received code vector is r and the party-check matrix is H, then the syndrome vector can be given as

$s=r{H}^T$

$=\left[001110\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 1& 1& 0\\ 0& 1& 1\\ 1& 0& 1\end{array}\right]=\left[100\right]$

Note: In the problems related to linear block codes use EX-OR operation, whenever there is an addition operation of bits.