An error correcting code has the following code words: 00000000, 00001111,…
2007
An error correcting code has the following code words:
00000000, 00001111, 01010101, 10101010, 11110000.
What is the maximum number of bit errors that can be corrected ?
- A.
0
- B.
1
- C.
2
- D.
3
Attempted by 372 students.
Show answer & explanation
Correct answer: B
Answer: 1 bit
Reasoning:
Compute Hamming distances between codewords. Distances include several pairs separated by 4 bits (for example, 00000000 vs 00001111 differ in 4 positions), and some pairs differ in 8 bits.
The minimum Hamming distance d_min among all codeword pairs is 4.
A code can correct up to t = floor((d_min - 1)/2) bit errors.
Thus t = floor((4 - 1)/2) = floor(1.5) = 1. The code can correct at most one bit error.
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