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Question

# In a linear block code (LBC):(n,k,dmin),n represents the number of bits in each codeword, k represents the number of bits in each message word and dmin 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)
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B
(7, 4, 3)
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C
(7, 6, 2)
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D
(6, 5, 2)
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Solution

## The correct option is B (7, 4, 3)Maximum distance seperable(MDS) codes satisfy the singleton bound. Singleton bound, dmin=n−k+1 For (6, 1, 6) ⇒n−k+1=6 and dmin=6 For (6, 5, 2) ⇒n−k+1=2 and dmin=2 For (7, 6, 2) ⇒n−k+1=2 and dmin=2 For (7, 4, 3) ⇒n−k+1=4 and dmin=3 So, the code is option (d) is not an MDS code.

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