Berlekamp–Massey algorithm: Difference between revisions

Revision as of 17:17, 30 October 2021

Revision as of 20:15, 21 November 2021

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{{distinguish|Berlekamp's algorithm}}

The '''Berlekamp–Massey algorithm''' is an [[algorithm]] that will find the shortest [[linear -feedback shift register]] (LFSR) for a given binary output sequence. The algorithm will also find the [[Minimal polynomial (field theory)|minimal polynomial]] of a linearly [[Recurrence relation|recurrent sequence]] in an arbitrary [[field (mathematics)|field]]. The field requirement means that the Berlekamp–Massey algorithm requires all non-zero elements to have a multiplicative inverse.<ref>{{Harvnb|Reeds|Sloane|1985|p=2}}</ref> Reeds and Sloane offer an extension to handle a [[ring (mathematics)|ring]].<ref>{{Citation |last1=Reeds |first1=J. A. |last2=Sloane |first2=N. J. A. |author-link2=N. J. A. Sloane |journal=SIAM Journal on Computing |volume=14 |issue=3 |pages=505–513 |year=1985 |title=Shift-Register Synthesis (Modulo n) |url=http://neilsloane.com/doc/Me111.pdf |doi=10.1137/0214038 |citeseerx=10.1.1.48.4652 }}</ref>

[[Elwyn Berlekamp]] invented an algorithm for decoding [[BCH code|Bose–Chaudhuri–Hocquenghem (BCH) codes]].<ref>{{Citation

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* [[Reed–Solomon error correction]]

* [[Reeds–Sloane algorithm]], an extension for sequences over integers mod&nbsp;''n''

* [[Nonlinear-feedback shift register] (NLFSR)

* [[NLFSR]], Non-Linear Feedback Shift Register

==References==