Berlekamp–Massey algorithm

The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field.

[3][4] James Massey recognized its application to linear feedback shift registers and simplified the algorithm.

The Berlekamp–Massey algorithm is an alternative to the Reed–Solomon Peterson decoder for solving the set of linear equations.

The formula L = (n + 1 − L) limits L to the number of available syndromes used to calculate discrepancies, and also handles the case where L increases by more than 1.

In the case of binary GF(2) BCH code, the discrepancy d will be zero on all odd steps, so a check can be added to avoid calculating it.