Error evaluator polynomial
= Error evaluator polynomial
{title2=$\Omega(z)$}
For errors $E_i$ at distinct nonzero locations $X_i$, the evaluator associated with syndromes $S_\ell=\sum_i E_iX_i^{b+\ell}$ is $\Omega(z)=\sum_i E_iX_i^b\prod_{h\ne i}(1-X_hz)$. Its degree is smaller than the number of errors. Together with the <error locator polynomial> it gives the <Reed-Solomon key equation> and the <Forney algorithm> for error magnitudes.