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.

Solved by gpt-5.6-sol high.