Geodesic
Unitary polylinear shift registers and their periods
Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 30-59

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In the article, a concept of a $k$-linear shift register ($k$-LSR) over a module ${}_RM$, where $R$ is an Artinian commutative ring, is studied. Such register is determined by a monic ideal $I\triangleleft R[x_1,\ldots,x_k]$ and a Ferrer diagram $\mathcal F\subset\mathbf N_0^k$. A class of ideals $I$ determining a $k$-LSR on some Ferrer diagram is described. In particular, a class of ideals $I$ determining a $k$-LSR on a fixed Ferrer diagram is constructed. A lower estimate for the periods of the constructed $k$-LSRs is obtained. It is shown that this estimate is attainable in some cases. 
@article{DM_2002_14_1_a3,
     author = {D. A. Mikhailov},
     title = {Unitary polylinear shift registers and their periods},
     journal = {Diskretnaya Matematika},
     pages = {30--59},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_1_a3/}
}
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D. A. Mikhailov. Unitary polylinear shift registers and their periods. Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 30-59. http://geodesic.mathdoc.fr/item/DM_2002_14_1_a3/