First, define an infinite-degree syndrome polynomial
Then, define the error magnitude polynomial as follows:
Given that we know only the first 2t coefficients of S(x), the
decoding problem becomes one of finding a polynomial 
of
degree less than or equal to t that satisfies
The error magnitudes are computed using the expression
Example: Double-error correction using the Berlekamp algorithm and a (7,3) Reed-Solomon code
Using the representation for GF(8), the following generator polynomial for the (7,3) RS code is obtained
Let the received polynomial be
.
Then compute the syndromes: 
and apply the Berlekamp algorithm.
The error-locator polynomial is
Compute the error magnitude polynomial:
The error locators are 
and 
. The
error magnitudes are found to be:
The error polynomial and the corresponding codeword:
