Editing Reed–Solomon error correction (section)

=== Berlekamp&ndash;Massey decoder ===
The [[Berlekamp&ndash;Massey algorithm]] is an alternate iterative procedure for finding the error locator polynomial. During each iteration, it calculates a discrepancy based on a current instance of Λ(''x'') with an assumed number of errors ''e'':
<math display="block"> \Delta  = S_{i} + \Lambda_1 \  S_{i-1} + \cdots + \Lambda_e \  S_{i-e}</math>
and then adjusts Λ(''x'') and ''e'' so that a recalculated Δ would be zero. The article [[Berlekamp&ndash;Massey algorithm]] has a detailed description of the procedure. In the following example, ''C''(''x'') is used to represent Λ(''x'').

==== Example ====

Using the same data as the Peterson Gorenstein Zierler example above:
{| class="wikitable"
|-
! ''n'' !! ''S''<sub>''n''+1</sub> !! ''d'' !! ''C'' !! ''B'' !! ''b'' !! ''m''
|-
| 0 || 732 || 732 || 197 ''x'' + 1 || 1 || 732 || 1
|-
| 1 || 637 || 846 || 173 ''x'' + 1 || 1 || 732 || 2
|-
| 2 || 762 || 412 || 634 ''x''<sup>2</sup> + 173 ''x'' + 1 || 173 ''x'' + 1 || 412 || 1
|-
| 3 || 925 || 576 || 329 ''x''<sup>2</sup> + 821 ''x'' + 1 || 173 ''x'' + 1 || 412 || 2
|}
The final value of ''C'' is the error locator polynomial, Λ(''x'').