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In the article, a concept of a k-linear shift register (k-LSR) over a module  R M, where R is an Artinian commutative ring, is studied. Such register is determined by a monic ideal I ◁ R[x 1 , ..., x k ] and a Ferrer diagram ℱ ⊂ N k  0 . 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.

Monic polylinear shift registers and their periods