= Forney algorithm
{c}
{title2=$E_i=-X_i^{1-b}\Omega(X_i^{-1})/\Lambda'(X_i^{-1})$}
{wiki}
For distinct error locations and the syndrome convention $S_\ell=\sum_i E_iX_i^{b+\ell}$, the displayed formula recovers the error magnitudes from the <error evaluator polynomial> and <error locator polynomial>. At $z=X_i^{-1}$, the evaluator is $E_iX_i^b\prod_{h\ne i}(1-X_h/X_i)$, whereas the locator's <formal derivative> is $-X_i\prod_{h\ne i}(1-X_h/X_i)$. Their quotient gives the formula; the denominator is nonzero because the locations are distinct.
// Target: polynomial.bigb
Back to article page
