Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
On the equivalence between Berlekamp's and Euclid's algorithms
IEEE Transactions on Information Theory
The inverses of block Hankel and block Toeplitz matrices
SIAM Journal on Computing
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
Mathematics of Computation
Matrix-free linear system solving and applications to symbolic computation
Matrix-free linear system solving and applications to symbolic computation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Black box linear algebra with the linbox library
Black box linear algebra with the linbox library
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
On the complexity of computing determinants
Computational Complexity
Shift-register synthesis and BCH decoding
IEEE Transactions on Information Theory
Relaxing order basis computation
ACM Communications in Computer Algebra
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We analyze the Matrix 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 [1994]. Our version of the algorithm makes no restrictions on the rank and dimensions of the matrix sequence. We also give new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator.