Berlekamp's Iterative Algorithm for Finding the Error-Locator Polynomial

1. Compute the syndrome sequence for the received word.
2. Initialize the algorithm variables: , and T(x)=x.
3. Set k=k+1. Compute the discrepancy as follows:

   

4. If , then go to step 8.
5. Modify the connection polynomial: .
6. If , then go to step 8.
7. Set L = k-L and .
8. Set .
9. If k < 2t, then go to step 3.
10. Determine the roots of . If the roots are distinct and lie in the right field, determine the error magnitudes, correct the corresponding locations in the received word, and STOP.
11. Declare a decoding failure and STOP.