Geodesic
Decomposition of polynomials using the shift-composition operation
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 68-82.

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V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.
Keywords: homomorphism, shift-composition operation, skew polynomials, finite fields, Galois ring. 
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V. I. Nozdrunov. Decomposition of polynomials using the shift-composition operation. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 68-82. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a6/

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