Final answer:
The minimum Hamming distance to detect 5 errors is 6, and to correct 5 errors is 11. These values are derived using simple formulas based on the number of errors to be detected or corrected.
Step-by-step explanation:
To determine the minimum Hamming distance for detecting and correcting errors in a bit stream, we use different formulas. For detecting d errors, the minimum Hamming distance h required is simply d + 1. However, for correcting errors, the formula is a bit more complex.
The minimum Hamming distance required to correct e errors in a bit stream is given by the formula h = 2e + 1. This ensures that even if there are e errors, the original message can still be recovered.
- For detecting 5 errors: h = d + 1, thus h = 5 + 1 = 6.
- For correcting 5 errors: h = 2e + 1, thus h = 2(5) + 1 = 11.
In summary, the minimum Hamming distance for detecting 5 errors is 6, and for correcting 5 errors, it is 11.