James L. Massey

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.^[ref]

A sequence that satisfies $s_n=c_1{s}_{n-1}+\cdots +c_L{s}_{n-L}$ 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.