Geodesic
On some classes of nonlinear shift registers with the same cyclic structure
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 96-119

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The paper is devoted to investigating the cyclic structure of an autonomous automaton $R(t)=R(G^n,\delta_f)$ named a shift register with feedback function $f$, $f\colon G^n\to G$, and transition function $$ \delta_f(y_1,y_2,\dots,y_n)=(y_2,y_3,\dots,y_n,f(y_1,y_2,\dots,y_n)). $$ An important problem in this field of investigation consists of constructing a nonlinear automaton $R(f)$ of a given cyclic structure, in particular, possessing a cycle of length $2^n$ or $2^n-1$. 
@article{DM_2010_22_2_a7,
     author = {M. I. Rozhkov},
     title = {On some classes of nonlinear shift registers with the same cyclic structure},
     journal = {Diskretnaya Matematika},
     pages = {96--119},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a7/}
}
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M. I. Rozhkov. On some classes of nonlinear shift registers with the same cyclic structure. Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 96-119. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a7/