Forney algorithm

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

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


Formal derivative

Λ'(x) is the 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)

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