Geodesic
Linear decomposition of discrete functions in terms of shift-composition operation
Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 115-143 
I. V. Cherednik. Linear decomposition of discrete functions in terms of shift-composition operation. Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 1, pp. 115-143. http://geodesic.mathdoc.fr/item/MVK_2020_11_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the shift-composition operation on discrete functions that arise in connection with homomorphisms of shift registers. For an arbitrary function over a finite field all possible representations in the form of shift-compositions of two functions (where the right function is linear) are described. Besides, the possibility to represent an arbitrary function as a shift-composition of three functions such that both left and right functions are linear is studied. It is proved that in the case of a simple field for linear functions and quadratic functions that are linear in the extreme variable the concepts of reducibility and linear reducibility coincide.

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