Question

In a linear block code $\left(LBC\right):(n,k,d_{min}),n$ represents the number of bits in each codeword, $k$ represents the number of bits in each message word and $d_{min}$ reppresents the minimum distance of code. Among the following LBCs, select the one which is not a maximum distance seperable (MDS) code.

• A. (6, 1, 6)
• B. (7, 4, 3)
• C. (7, 6, 2)
• D. (6, 5, 2)

Answer 1

The correct option is B (7, 4, 3)

Maximum distance seperable(MDS) codes satisfy the singleton bound.
Singleton bound, $d_{min}=n-k+1$
For (6, 1, 6) $\Rightarrow n-k+1=6$ and $d_{min}=6$
For (6, 5, 2) $\Rightarrow n-k+1=2$ and $d_{min}=2$
For (7, 6, 2) $\Rightarrow n-k+1=2$ and $d_{min}=2$
For (7, 4, 3) $\Rightarrow n-k+1=4$ and $d_{min}=3$
So, the code is option (d) is not an MDS code.