Analysis of the Berlekamp-Massey Linear Feedback Shift-Register Synthesis Algorithm

An analysis of the Berlekamp-Massey Linear Feedback Shift-Register (LFSR) Synthesis Algorithm is provided which shows that an input string of length n requires O(n
²
) multiplication/addition operations in the underlying field of definition. We also derive the length distribution for digit strings of length n. Results show that, on the average, the encoded length is no greater than n + 1 Furthermore, we exhibit a connection between step 1 of the Ling-Palermo algorithm and the LFSR Algorithm, and the LFSR Algorithm turns out to be computationally superior.