Until the discovery of better coding techniques (Turbo codes and low-density parity codes), Reed-Solomon forward error correction (FEC) was one of the most powerful ways to make data storage or data transmission resilient against corruption - Reed-Solomon Error Correcting Codes from the Bottom Up

• Luhn algorithm - a simple check digit formula used to validate a variety of identification numbers. Designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers.

• Error Detection - cover different schemes and usage.

see also

• Error correction and concealment in the Compact Disc system (1982) [pdf]