What are the most obvious generalizations of Berlekamp Massey algorithm [1] to matrix sequences?



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> [1] [Massey, J. L.](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.9932), "Shift-register synthesis and BCH decoding", IEEE Trans. Information Theory IT-15 (1): 122–127
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Matrix version of Berlekamp Massey algorithm
You might find [this](http://repository.lib.ncsu.edu/ir/handle/1840.16/3825) dissertation interesting. The author has collected many references of the Matrix versions of the Berlekamp-Massey algorithm (citing Rissansen, Dickinson, Thome and other papers) and its applications. 


