= James L. Massey
{c}
<James L. Massey> showed that Berlekamp's iterative BCH-decoding algorithm solves a general register-synthesis problem: find a shortest <linear-feedback shift register> generating a prescribed finite sequence. His 1969 paper derives the algorithm through the lengths and discrepancies of successive candidate recurrences, connecting the <Berlekamp-Massey algorithm> to error correction.<Shift-Register Synthesis and BCH Decoding by James L. Massey>[§§II–V]{ref}
A sequence that satisfies $s_n=c_1s_{n-1}+\cdots+c_Ls_{n-L}$ can be generated from $L$ stored symbols and feedback coefficients over a field. A newly observed symbol may contradict the current recurrence; the algorithm then updates the candidate using a prior discrepancy. Minimal synthesis is therefore more than finding some recurrence that happens to fit the observations.
Back to article page
