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Joined 2026-09-21 Message
Incoming links: Minimum-distance error-detection and correction guarantee
Past exam of the mathematics course of the University of Cambridge 2008 ii Paper 3 4G Solution Created 2026-09-24 Updated 2026-09-24
Past exam of the mathematics course of the University of Cambridge 2024 ii Paper 2 3K b Solution Created 2026-09-24 Updated 2026-09-25
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.