Question

A(5,2) linear block code is defined as,
C = {11001, 00111, 10010, 01010}
The minimum distance of the code $\left(d_{min}\right)$ is _______

• A. 2

Answer 1

The correct option is A 2
Let the codewords are named as
$c_1:\left(11001\right)$
$c_2:\left(00111\right)$
$c_3:\left(10010\right)$
$c_4:\left(01010\right)$

Codewords pair	Hamming distance
$c_1,c_2$	4
$c_1,c_3$	3
$c_1,c_4$	3
$c_2,c_3$	3
$c_2,c_4$	3
$c_3,c_4$	2

So the minimum distance $\left(d_{min}\right)$ of the given linear block code is 2.