Reed–Solomon Evaluation Code

Reed–Solomon codes protect digital data from errors by evaluating polynomials over a finite field. A short message forms the coefficients of a polynomial, which is then evaluated at multiple points. Because low-degree polynomials cannot intersect too many times without being identical, we can uniquely identify the original polynomial even if some evaluation points are corrupted.

Experiment

Use the interactive module to explore how error correction handles different levels of corruption.

1. Select the Message "General". Observe that the encoded word is [1, 6, 3, 6, 1].
2. Set the Error position to "2" and Error amount to "1". The received word changes to [1, 6, 4, 6, 1].
3. Observe the Decoded coefficients remain [1, 2, 3], matching our worked example. The nearest Hamming distance is 1.
4. Try selecting Error position "None" to see a clean transmission.