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

[1] Massey, J. L., "Shift-register synthesis and BCH decoding", IEEE Trans. Information Theory IT-15 (1): 122–127

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"displacement rank" should bring up quite a number of interesting papers... – J. M. Dec 11 2010 at 3:57

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You might find this 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.

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