Maths and computer science · Solid · Dissertation or artefact

How QR codes survive damage: a maths EPQ idea

Why it works as an EPQ

Parity checks and Hamming codes are learnable and testable, and lead naturally to the codes used in QR codes.

Scope and difficulty

Solid. Solid. Hamming codes fully; Reed–Solomon codes described rather than derived.

The maths

Builds on these A Level topics: Algebra and functions · Probability.

You would learn:

• Parity and check digits
• Hamming distance and Hamming codes
• Binary arithmetic

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Explain check digits (for example on books) and what errors they catch.
2. Build the Hamming (7,4) code and prove it corrects one error.
3. Test it by flipping bits at random in code.
4. Explain how stronger codes allow QR codes to survive damage, and judge the trade-off with data size.

Pitfalls

• Not separating error detection from correction.
• Claims about QR versions without a source.

Where to start reading

• Search for: Hamming 7,4 code explained
• Search for: QR code error correction levels Reed-Solomon

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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All maths and computer science ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.