GATE 2017 CS (CS2) – Question 44

Computer Networks · Data Link Layer: Error Detection, Medium Access Control, Flow Control · 2 marks · Multiple choice

A binary code has exactly four valid words: 00000,01011,10101,11110. Let p be minimum Hamming distance and q maximum correctable bit errors. Find p,q.

p=3,q=1
p=3,q=2
p=4,q=1
p=4,q=2

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Correct answer: (A) p=3,q=1

Explanation

Pairwise XOR weights are 3,3,4,4,3,3, so dₘᵢₙ=p=3. Unique correction of t errors requires 2t+1≤dₘᵢₙ, giving $q=\lfloor(3-1)/2\rfloor=1$. Thus A.

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