On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)


The Berlekamp–Massey and Berlekamp–Massey–Sakata algorithms compute a minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional array. In this paper some underlying properties of and connections between these two algorithms are clarified theoretically: a unified flow chart for both algorithms is proposed to reveal their connections; the polynomials these two algorithms maintain at each iteration are proved to be reciprocal when both algorithms are applied to the same sequence; and the uniqueness of the choices of polynomials from two critical polynomial sets in the Berlekamp–Massey–Sakata algorithm is investigated.


Berlekamp–Massey algorithm Berlekamp–Massey–Sakata algorithm Minimal polynomial Reciprocal polynomial 



The authors would like to thank the anonymous reviewers for their helpful suggestion which contribute to considerable improvement of this paper.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LMIB–School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.Beijing Advanced Innovation Center for Big Data and Brain ComputingBeihang UniversityBeijingChina

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