# Forney algorithm

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

## Contents

## Formal derivative

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

In the above expression, note that *i* is an integer, and λ_{i} 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.

## Derivation

Lagrange interpolation gives a derivation of the Forney algorithm.

## Erasures

Define the erasure locator polynomial

Where the erasure locations are given by *j _{i}*. Apply the procedure described above, substituting Γ for Λ.

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