This article is cited in 7 papers

Unitary polylinear shift registers and their periods

D. A. Mikhailov


Abstract: 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.

UDC: 512.62

Received: 11.09.2001

DOI: 10.4213/dm229

 English version: Discrete Mathematics and Applications, 2002, 12:1, 15–44

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