Geodesic
Linear decomposition of discrete functions in terms of shift-composition operation
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 68-73

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We investigate the shift-composition operation of discrete functions that arises under shift register's homomorphisms. For an arbitrary function over a finite field, all right linear decompositions are described in terms of shift-composition. Moreover, we study the possibility for representing an arbitrary function by a shift-composition of three functions such that both external functions are linear. It is proved that in the case of a simple field, the concepts of reducibility and linear reducibility coincide for linear functions and quadratic functions that are linear in the external variable.
Keywords: discrete functions, finite fields, shift register, shift-composition. 
@article{PDMA_2019_12_a20,
     author = {I. V. Cherednik},
     title = {Linear decomposition of discrete functions in terms of shift-composition operation},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {68--73},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a20/}
}
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I. V. Cherednik. Linear decomposition of discrete functions in terms of shift-composition operation. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 68-73. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a20/