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Reed-Solomon Codes

The error-correcting code that reconstructs lost data by over-sampling a polynomial, used everywhere from CDs to QR codes to spacecraft.

[!todo] Seed note. A starting point, not a finished note yet.

Reed-Solomon is a block error-correcting code invented by Irving Reed and Gustave Solomon in 1960. It treats a message as the coefficients of a polynomial over a finite field, then transmits evaluations of that polynomial at more points than the message needs. Because the polynomial is over-determined, the original data can be recovered exactly even when a bounded number of symbols are corrupted, and it corrects erasures (errors at known positions) at twice the rate of errors at unknown positions. It is the workhorse behind CDs, DVDs, QR codes, deep-space telemetry, and the ECC200 Data Matrix, where it is what lets a marked part stay readable after real physical damage. Seeded from ECC200.

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