@article{SAKATA1988321,
    Abstract = {We present an algorithm for finding a minimal set of two-dimensional linear recurring relations capable of generating a prescribed finite two-dimensional array. This is a two-dimensional extension of the Berlekamp-Massey algorithm for synthesizing a shortest linear feedback shift-register capable of generating a given finite sequence. The complexity of computation for an array of size n is 0(n2) under some reasonable assumptions. Furthermore, we make clear some relationship between our algorithm and Gr{\"o}bner bases of bivariate polynomial ideals, where polynomials correspond one-to-one to linear recurring relations.},
    Author = {Sakata, Shojiro},
    File = {Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array - 1-s2.0-S0747717188800336-main - a - n.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Number = {3},
    Pages = {321 - 337},
    Title = {Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array},
    URL = {http://www.sciencedirect.com/science/article/pii/S0747717188800336},
    Volume = {5},
    Year = {1988},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717188800336},
    bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(88)80033-6},
    date-added = {2020-09-14 15:35:30 +0200},
    date-modified = {2020-09-14 15:35:30 +0200},
    doi = {10.1016/S0747-7171(88)80033-6}
}

@article{SAKATA1988321, Abstract = {We present an algorithm for finding a minimal set of two-dimensional linear recurring relations capable of generating a prescribed finite two-dimensional array. This is a two-dimensional extension of the Berlekamp-Massey algorithm for synthesizing a shortest linear feedback shift-register capable of generating a given finite sequence. The complexity of computation for an array of size n is 0(n2) under some reasonable assumptions. Furthermore, we make clear some relationship between our algorithm and Gr{\"o}bner bases of bivariate polynomial ideals, where polynomials correspond one-to-one to linear recurring relations.}, Author = {Sakata, Shojiro}, File = {Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array - 1-s2.0-S0747717188800336-main - a - n.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Number = {3}, Pages = {321 - 337}, Title = {Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array}, URL = {http://www.sciencedirect.com/science/article/pii/S0747717188800336}, Volume = {5}, Year = {1988}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0747717188800336}, bdsk-url-2 = {https://doi.org/10.1016/S0747-7171(88)80033-6}, date-added = {2020-09-14 15:35:30 +0200}, date-modified = {2020-09-14 15:35:30 +0200}, doi = {10.1016/S0747-7171(88)80033-6} }