On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms
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.
KeywordsBerlekamp–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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