Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/3k/b/solution

The added bit is the overall parity bit. The original minimum-weight words have weight three, so they acquire a parity bit equal to one and have extended weight four. Every original even-weight difference keeps its weight, while every odd-weight difference gains one; hence the new minimum distance is four.
The minimum-distance error-detection and correction guarantee therefore says that the code detects three errors and corrects one error.

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