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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - I. V. Cherednik
TI  - Linear decomposition of discrete functions in terms of shift-composition operation
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2019
SP  - 68
EP  - 73
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2019_12_a20/
LA  - ru
ID  - PDMA_2019_12_a20
ER  - 
%0 Journal Article
%A I. V. Cherednik
%T Linear decomposition of discrete functions in terms of shift-composition operation
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2019
%P 68-73
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2019_12_a20/
%G ru
%F PDMA_2019_12_a20
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/

[1] Solodovnikov V. I., Registry sdviga i kriptoalgoritmy na ikh osnove, LAP LAMBERT Academic Publishing, 2017

[2] Solodovnikov V. I., “Gomomorfizmy registrov sdviga v lineinye avtomaty”, Diskretnaya matematika, 2008, no. 4, 87–101 | MR

[3] Lidl R., Niderraiter G., Konechnye polya, Mir, M., 1988 | MR

[4] Solodovnikov V. I., “Gomomorfizmy dvoichnykh registrov sdviga”, Diskretnaya matematika, 2005, no. 1, 73–88 | DOI | MR | Zbl

[5] Kuzmin A. S., Nechaev A. A., Shishkin V. A., “Bent- i giperbent-funktsii nad konechnym polem”, Trudy po diskretnoi matematike, 2007, no. 10, 97–122

[6] Cheremushkin A. V., “Additivnyi podkhod k opredeleniyu stepeni nelineinosti diskretnoi funktsii”, Prikladnaya diskretnaya matematika, 2010, no. 2, 22–33