Let C be a binary linear code with minimum distance \(2t + 1\) then it can…
2017
Let C be a binary linear code with minimum distance \(2t + 1\) then it can correct upto _____ bits of error.
- A.
\(t + 1\) - B.
\(t\) - C.
\(t – 2\) - D.
\(\frac t 2\)
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Correct answer: B
Key formula: A code with minimum distance d can correct up to floor((d - 1) / 2) errors.
Apply the formula with d = 2t + 1:
Compute d - 1 = (2t + 1) - 1 = 2t.
Divide by 2: (d - 1) / 2 = 2t / 2 = t.
Taking the floor does not change the value since t is an integer, so the maximum correctable errors = t.
Therefore, a binary linear code with minimum distance 2t + 1 can correct up to t bit errors.