Forney algorithm

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In [[coding 1}}, so the expression simplifies to:

e_j = - \frac{\Omega(X_j^{-1})}{\Lambda'(X_j^{-1})}

Formal derivative[edit]

Λ'(x) is the formal derivative of the error locator polynomial Λ(x):

\Lambda'(x) = \sum_{i=1}^{\nu} i \, \cdot \, \lambda_i \, x^{i-1}

In the above expression, note that i is an integer, and λi would be an element of the finite field. The operator · represents ordinary multiplication (repeated addition in the finite field) and not the finite field's multiplication operator.


Lagrange interpolation gives a derivation of the Forney algorithm.


Define the erasure locator polynomial

\Gamma(x) = \prod (1- x \, \alpha^{j_i})

Where the erasure locations are given by ji. Apply the procedure described above, substituting Γ for Λ.

If both errors and erasures are present, use the error-and-erasure locator polynomial

\Psi(x) = \Lambda(x) \, \Gamma(x)

See Also on BitcoinWiki[edit]