Reed-Solomon Error Correction

A Complete Reed-Solomon Encoding and Decoding Example

By Hugo Lyppens

Dr. Dobb's Journal January 1997

Generator polynomial: 54 + 01x^1 + F3x^2 + 6Cx^3 + 1Bx^4 + 5Fx^5 + 62x^6 + D4x^7 + B2x^8 + CFx^9 + 1Ex^10 + 72x^11 + BAx^12 + F4x^13 + E7x^14 + 81x^15 + 01x^16
  
  Enter original string or enter empty string to quit:
  Coding theory is fun!
  Enter string with up to 8 symbol errors or enter empty
  string to quit:
  C0ding th.ory is f&n?
  Syndrome 0: 59
  Syndrome 1: 8d
  Syndrome 2: 5d
  Syndrome 3: 4d
  Syndrome 4:  5
  Syndrome 5: bf
  Syndrome 6: ae
  Syndrome 7: 5c
  Syndrome 8: 18
  Syndrome 9: ad
  Syndrome 10: 6b
  Syndrome 11: b4
  Syndrome 12: c9
  Syndrome 13: c3
  Syndrome 14: e6
  Syndrome 15: fe
  
  Degree of err. loc. polynomial: 4
  Error locator polynomial: CC  + B8x^1 + 05x^2 + 21x^3 +
  3Cx^4
  Error evaluator polynomial: 5C  + 2Fx^1 + 4Dx^2 + ADx^3
  number of roots of elp: 4
  correcting error at location 20 of magnitude 1E
  correcting error at location 9 of magnitude 4B
  correcting error at location 1 of magnitude 5F
  correcting error at location 18 of magnitude 53
  Decoding OK, recovered `Coding theory is fun!' from
  `C0ding th.ory is f&n?' by correcting 4 errors!

Figure 3: Program output.