The message bytes are coefficients of m(x). The encoder appends the remainder of m(x)·x^n−k ÷ g(x), so the full codeword c(x) is divisible by the generator g(x) = (x−α⁰)(x−α¹)…(x−α^n−k−1).

Click any byte to corrupt it with a random value, or switch to Erasure to flag it as unreadable. Click again to restore it. Shift-click always toggles an erasure.

Each bar is |Λ(X_p⁻¹)| for byte position p. A root (value 0, green marker) means p is an error location. Violet markers are the erasures you flagged, which the decoder already knows.