The code words at the output of channel encoder of a (6, 2) linear block code (LBC) are given as follows:

$c_{0} = [000000]; c_{1} = [010010]; c_{2} = [101101]; c_{3} = [111111]$

The minimum distance $(d_{m i n})$ of the given LBC is equal to_______
2

Open in App

Solution

The correct option is A 2
The minimum distance $(d_{m i n})$ of a code can be defined as
''The smallest value of the Hamming distance between any pair of code words in the given coding system''

or

''The smallest Hamming weight of non-zero code words in the given coding system''

For the given code,

$c_{i}$ Code word Hamming weight of the code word

$c_{0}$ 000000 0

$c_{1}$ 010010 2

$c_{2}$ 101101 4

$c_{3}$ 111111 6

From the above table, it is clear that the smallest Hamming weight of non-zero code word is 2.

So, the minimum distance $(d_{m i n})$ of the given LBC is 2.

Suggest Corrections

Similar questions

C_{0} = [000000]; C_{1} = [010010]; c_{2} = [101101]; C_{3} = [111111]

d_{m i n} = 4

H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 & 0 & 0 0 & 1 & 0 & 1 & 0 0 & 1 & 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

(L B C) : (n, k, d_{m i n}), n

k

d_{m i n}

G = {⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 & 1 & 1 & 0 0 & 1 & 0 & 0 & 1 & 1 0 & 0 & 1 & 1 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦}_{3 \times 6}

Join BYJU'S Learning Program

$c_{i}$	Code word	Hamming weight of the code word
$c_{0}$	000000	0
$c_{1}$	010010	2
$c_{2}$	101101	4
$c_{3}$	111111	6