GATE CS 2017 Set 2 — Question 34
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Computer Networks → Data Link Layer → Error Correction (Hamming)
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Question
Consider a binary code that consists of only four valid codewords as given below:00000, 01011, 10101, 11110Let the minimum Hamming distance of the code be and the maximum number of erroneous bits that can be corrected by the code be . Then the values of and are
Correct answer
(A) p=3 and q=1
Solution
1.Identify the codewords: .
2.Calculate Hamming distances between all pairs:
- (bits 2, 4, 5 differ)
- (bits 1, 3, 5 differ)
- (bits 1, 2, 3, 4 differ)
- (bits 1, 2, 3, 4 differ)
- (bits 1, 3, 5 differ)
- (bits 2, 4, 5 differ)
4.Determine : The error correction capability is given by .
Thus, and .Continue learning with Success Tracker
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