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Berlekamp–Massey Algorithm
[chapter]

2011
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Encyclopedia of Cryptography and Security
*

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Generalised Berlekamp–Massey algorithm

2002
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IEE Proceedings - Communications
*

It further enables the presentation of a generalised

doi:10.1049/ip-com:20020413
fatcat:qkkluv2d3zhqdjztikkvk6dzdu
*Berlekamp**Massey**algorithm*, including the conventional*algorithm*and the inversion-free*algorithm*as two special cases. ... The BerlekampMassey*algorithm*is revisited and proven again by using the matrix representation. ... Introduction The*Berlekamp*-*Massey**algorithm*(BMA) [I. 21 is an efficient method for determining the error-locator polynomial in decoding the Reed-Solomon and BCH codes. ...##
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The Berlekamp-Massey Algorithm revisited

2006
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Applicable Algebra in Engineering, Communication and Computing
*

We propose a slight modification of the

doi:10.1007/s00200-005-0190-z
fatcat:qzlaz2af3zamloghnncwjoca5a
*Berlekamp*-*Massey**Algorithm*for obtaining the minimal polynomial of a given linearly recurrent sequence. ... Next, we introduce our modified*Berlekamp*-*Massey**Algorithm*in pseudocode (*Algorithm*2):*Algorithm*2 Modified*Berlekamp*-*Massey**Algorithm*Input: n ∈ N. ... That proves that our modification of*Berlekamp*-*Massey**Algorithm*is right. ...##
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On the matrix berlekamp-massey algorithm

2013
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ACM Transactions on Algorithms
*

We analyze the Matrix

doi:10.1145/2500122
fatcat:w4xakdv63zglhkdaa5wp5kw3wu
*Berlekamp*/*Massey**algorithm*, which generalizes the*Berlekamp*/*Massey**algorithm*[*Massey*1969] for computing linear generators of scalar sequences. ... The Matrix*Berlekamp*/*Massey**algorithm*computes a minimal matrix generator of a linearly generated matrix sequence and has been first introduced by Rissanen [1972a] , Dickinson et al. [1974], and Coppersmith ... Matrix*Berlekamp*/*Massey**algorithm*will compute a minimal generator. ...##
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The Berlekamp-Massey Algorithm via Minimal Polynomials
[article]

2010
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arXiv
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pre-print

Taking reciprocals gives a '

arXiv:1001.1597v3
fatcat:xpsbkzry2zamhb5xo7z6afd3se
*Berlekamp*-*Massey*theorem' i.e. a recursive construction of the polynomials arising in the*Berlekamp*-*Massey**algorithm*, relative to any element of D. ... The recursive theorem readily yields the iterative minimal polynomial*algorithm*due to the author and a transparent derivation of the iterative*Berlekamp*-*Massey**algorithm*. ... 1 Introduction The*Berlekamp*-*Massey*(BM)*Algorithm*The BM*algorithm*determines a linear recurrence of least order L ≥ 0 which generates a given (finite) sequence s of length n ≥ 1 over a field F, [13 ...##
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A fraction free Matrix Berlekamp/Massey algorithm

2013
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Linear Algebra and its Applications
*

We describe a fraction free version of the Matrix

doi:10.1016/j.laa.2013.06.016
fatcat:5j7qpgywwzhnleooa6ckcrdltm
*Berlekamp*/*Massey**algorithm*. The*algorithm*computes a minimal matrix generator of linearly generated square matrix sequences over an integral domain. ... For scalar sequences, the matrix*algorithm*specializes to a more efficient*algorithm*than the*algorithm*currently in the literature. ... Fraction Free Matrix*Berlekamp*/*Massey**Algorithm*We begin by describing the fraction free Matrix*Berlekamp*/*Massey**algorithm*. ...##
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New serial architecture for the Berlekamp-Massey algorithm

1999
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IEEE Transactions on Communications
*

We propose a new efficient serial architecture to implement the

doi:10.1109/26.764911
fatcat:jnuyylpphrdovn24mgzyhqhg2e
*Berlekamp*-*Massey**algorithm*, which is frequently used in BCH and Reed-Solomon decoders. ... An inversionless*Berlekamp*-*Massey**algorithm*is adopted which not only eliminates the finite-field inverter but also introduces additional parallelism. ... of the inversionless*Berlekamp*-*Massey**algorithm*, which is shown in Fig. 2 . ...##
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Extension of the Berlekamp-Massey algorithm to N dimensions

1990
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Information and Computation
*

INTRODUCTION In the previous paper (Sakata, 1988) , we gave an extension of the BerlekampMassey

doi:10.1016/0890-5401(90)90039-k
fatcat:gtwevola2vblbmnwjmcrnuhdji
*algorithm*(*Berlekamp*, 1968;*Massey*, 1969) to two dimensions. ... we restrict W(u) to be the class of minimal polynomial sets F composed of "manic" polynomials f in "reduced normal form" in the sense that for any .fe F, Tfs {Deg(f) ) u d(F), where such reduction can*BERLEKAMP*-*MASSEY*...##
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A simple Hankel interpretation of the Berlekamp-Massey algorithm

1989
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Linear Algebra and its Applications
*

A simple interpretation of the

doi:10.1016/0024-3795(89)90032-3
fatcat:ds4bnn4ijrfi7kb7bwhglgz4qy
*Berlekamp*-*Massey**algorithm*in the light of the Hankel matrix is presented. ... Next, the Hankel system of equations that yields the updated connection polynomial is solved via the natural LU factorization of the Hankel matrix, which itself leads to the*Berlekamp*-*Massey**algorithm*... An earlier successful attempt to make the*Berlekamp*-*Massey**algorithm*more understandable is due to Imamura and Yoshida [3] . ...##
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ON THE BERLEKAMP — MASSEY ALGORITHM AND ITS APPLICATION FOR DECODING ALGORITHMS

2021
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Vestnik of Samara University Natural Science Series
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*Algorithms*for decoding the listed codes based on the

*Berlekamp*

*Massey*

*algorithm*are given. ... An optimized

*Berlekamp*

*Massey*

*algorithm*is also given for the case ofa field of characteristic 2. ... On the

*Berlekamp*-

*Massey*

*algorithm*and its application...Пусть на приемном конце получен вектор:v = (1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1), в котором до двух ошибок (как видно, стирающих символов ...

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The Berlekamp-Massey Algorithm and the Euclidean Algorithm: a Closer Link
[article]

2009
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arXiv
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pre-print

This results in a new, simpler, and compacter presentation of the

arXiv:0908.2198v1
fatcat:e3x47pxazzcufif7z6dugixdke
*Berlekamp*-*Massey**algorithm*. ... The two primary decoding*algorithms*for Reed-Solomon codes are the*Berlekamp*-*Massey**algorithm*and the Sugiyama et al. adaptation of the Euclidean*algorithm*, both designed to solve a key equation. ... From the Euclidean to the*Berlekamp*-*Massey**algorithm*In this section we will see that the previous*algorithm*and the*Berlekamp*-*Massey**algorithm*are essentially the same. ...##
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Universal Reed-Solomon decoders based on the Berlekamp-Massey algorithm

2004
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Proceedins of the 14th ACM Great Lakes symposium on VLSI - GLSVLSI '04
*

Universal field inversions and divisions are not discussed in this paper since the an inversion-less

doi:10.1145/988952.988965
dblp:conf/glvlsi/YanS04
fatcat:oojsaizm2jefzis5qc26dexkc4
*Berlekamp*-*Massey**algorithm*is used to solve the key equation. ... Furthermore, the scaling factors cancel out in Forney's formula, used to evaluate error values, and thus correct error values can be obtained from the universal*Berlekamp*-*Massey**algorithm*. ... Sarwate and Shanbhag proposed a reformulated*Berlekamp*-*Massey**algorithm*and designed high-speed RS decoder architectures based on the reformulated*algorithm*[10] . ...##
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Berlekamp—Massey Algorithm, Continued Fractions, Pade Approximations, and Orthogonal Polynomials

2006
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Mathematical Notes
*

The

doi:10.1007/s11006-006-0004-z
fatcat:jbjqtepeb5bfdni7chdhco34hi
*Berlekamp*-*Massey**algorithm*(further, the BMA) is interpreted as an*algorithm*for constructing Padé approximations to the Laurent series over an arbitrary field with singularity at infinity. ... THE*BERLEKAMP*-*MASSEY**ALGORITHM*(BMA) Let us show that the BMA simultaneously calculates both the elements a n (z) of the continued fraction in the case of an arbitrary series f (z) and the sequence Q n ... Suppose that Λ i = c (i) L i (f ) x L i (f ) + · · · + c (i) 1 x + c (i) 0 , c (i) 0 = 1, i = 1, . . . , k ;*BERLEKAMP*-*MASSEY**ALGORITHM*45 then, by definition, s i=1 c (k) i f j−i = f j for j = s, . . ...##
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Analysis of the Berlekamp-Massey Linear Feedback Shift-Register Synthesis Algorithm

1976
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IBM Journal of Research and Development
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An analysis of the

doi:10.1147/rd.203.0204
fatcat:a4jas7k2srdh3hvkiqkpsquqha
*Berlekamp*-*Massey*Linear Feedback Shift-Register (LFSR) Synthesis*Algorithm*is provided which shows that an input string of length 12 requires C ( i 2 ) multiplication/ addition operations ... Furthermore, we exhibit a connection between step 1 of the Ling-Palermo*algorithm*and the LFSR*Algorithm*, and the LFSR*Algorithm*turns out to be computationally superior. ... The LFSR*algorithm*, which is essentially the same as the*Berlekamp*Iterative*Algorithm*[ 31, was developed for encoding and is more general and computationally faster than the BOIC scheme. ...##
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Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm

2002
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Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02
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THE FRACTION-FREE

doi:10.1145/780506.780519
dblp:conf/issac/GiesbrechtKL02
fatcat:stbmtl4tcbewllqivxe5mfpuj4
*BERLEKAMP*/*MASSEY**ALGORITHM*The*Berlekamp*/*Massey**algorithm*[18] processes a sequence of elements a0, a1, . . . from a field K. ... By computing the corresponding*Berlekamp*/*Massey*quantities of the subresultant GCD*algorithm*, we obtain our fraction-free*Berlekamp*/*Massey**algorithm*, which outputs an integral multiple of the minimal generator ...
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