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Coding theory
Galois fields, worked by hand: GF(8) in one table
What a Galois field is, worked by hand: why mod 7 works and mod 8 fails, GF(8) built from x³ + x + 1, a full multiplication table, and GF(256) in QR and AES.
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Coding theory
Reed–Solomon error correction, worked by hand
How Reed–Solomon error correction works, step by step: encoding as a polynomial, rebuilding lost symbols, fixing a wrong one, and why it needs a finite field.
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Coding theory · Supply chain
A scratched label still scans, and that is not luck
A check digit tells you a barcode scan was wrong. Reed–Solomon parity tells you what it should have been. That difference decides what a damaged label costs.