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I'm trying to find a way to understand the process of the Berlekamp-Massey Algorithm. But I'm struggling in understanding the fourth step of the process, which is $B^{(r+1)}(x) = A^{(r)}/\delta^{(r)}$. I found this algorithm from this paper, "VLSI Architectures for Reed-Solomon Codes: Classic, Nested, Coupled, and Beyond". However, I don't know what this step is doing. Can anyone explain to me the purpose of having this step?

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Too long for a comment.

The Berlekamp Massey algorithm is a tour de force. It has the names of two Shannon award (top information/coding theory award for lifetime contributions) recipients attached and it is quite subtle.

The step you point to is a way of correcting the discrepancy between the sequence the current polynomial would generate and the actual sequence by modifying the polynomial.

Dilip Sarwate has a nice answer on this with somewhat different notation.

Berlekamp-Massey to construct minimal LFSR

The textbooks by Richard Blahut also explain the BM algorithm. The one called “Fast algorithms..” may be the most detailed.

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  • $\begingroup$ The explanation is based on the wikepedia derivation. That part i understand. However, this algorithm seems to correct the discrepancy in the future iteration. This part I'm confused. $\endgroup$
    – ytj_banana
    Commented Feb 6, 2021 at 21:27

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