## The Berlekamp-Massey Algorithm revisited

Citations: | 3 - 0 self |

### BibTeX

@MISC{Atti_theberlekamp-massey,

author = {Nadia Ben Atti},

title = {The Berlekamp-Massey Algorithm revisited},

year = {}

}

### OpenURL

### Abstract

We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation.

### Citations

439 |
Algebraic Coding Theory
- Berlekamp
- 1968
(Show Context)
Citation Context ... large literature can be consulted nowadays in relation to the Berlekamp’s Algorithm. The (original) Berlekamp’s Algorithm was created for decoding Bose-Chaudhuri-Hocquenghem (BCH) codes in 1968 (see =-=[1]-=-). One year later, the original version of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles,... |

274 |
Shift-register synthesis and BCH decoding
- MASSEY
- 1969
(Show Context)
Citation Context ...nal) Berlekamp’s Algorithm was created for decoding Bose-Chaudhuri-Hocquenghem (BCH) codes in 1968 (see [1]). One year later, the original version of this algorithm has been simplified by Massey (see =-=[5]-=-). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in [2],[3], [6], [9] and [10]. Some more recent interpretations of the BerlekampM... |

113 | A computational introduction to number theory and algebra
- Shoup
- 2008
(Show Context)
Citation Context ...re comprehensible and natural. We did not find in the literature such a modification before the first submission of this article (May 2004). However, we would like to add that you can also find it in =-=[8]-=-, published in 2005, without any reference. 2 Some good reasons to modify the usual algorithm By the one hand, as it can be observed at the end of Algorithm 1, we have to compute the (nearly) reverse ... |

25 |
On the Equivalence Between Berlekamp’s and Euclid’s Algorithms
- Dornstetter
- 1987
(Show Context)
Citation Context ... original version of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in [2],=-=[3]-=-, [6], [9] and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and [7]. The usual interpretation of the ... |

17 |
Continued fractions and Berlekamp’s algorithm
- Welch, Scholtz
- 2000
(Show Context)
Citation Context ...of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in [2],[3], [6], [9] and =-=[10]-=-. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and [7]. The usual interpretation of the Berlekamp-Massey Al... |

14 |
Continued fractions and linear recurrences
- MILLS
- 1975
(Show Context)
Citation Context ...inal version of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in [2],[3], =-=[6]-=-, [9] and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and [7]. The usual interpretation of the Berle... |

9 |
A simple Hankel interpretation of the Berlekamp-Massey algorithm. Linear Algebra and its Applications
- Jonckheere, Ma
- 1989
(Show Context)
Citation Context ...in several articles, for instance, in [2],[3], [6], [9] and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in =-=[4]-=- and [7]. The usual interpretation of the Berlekamp-Massey Algorithm for obtaining P (x) is expressed in pseudocode in Algorithm 1. In practice, we must apply the simplification of the extended Euclid... |

7 |
New techniques for the computation of linear recurrence coefficients. Finite Fields and their
- Pan
- 2000
(Show Context)
Citation Context ...al articles, for instance, in [2],[3], [6], [9] and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and =-=[7]-=-. The usual interpretation of the Berlekamp-Massey Algorithm for obtaining P (x) is expressed in pseudocode in Algorithm 1. In practice, we must apply the simplification of the extended Euclidean Algo... |

6 |
On the continued fraction and Berlekamp’s algorithm
- Cheng
- 1984
(Show Context)
Citation Context ... the original version of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in =-=[2]-=-,[3], [6], [9] and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and [7]. The usual interpretation of ... |

1 |
et al. A method for solving key equation for decoding Goppa codes
- Sugiyama
- 1975
(Show Context)
Citation Context ...version of this algorithm has been simplified by Massey (see [5]). The similarity of the algorithm to the extended Euclidean Algorithm can be found in several articles, for instance, in [2],[3], [6], =-=[9]-=- and [10]. Some more recent interpretations of the BerlekampMassey Algorithm in terms of Hankel Matrices and Padé approximations can be found in [4] and [7]. The usual interpretation of the Berlekamp-... |