Geodesic
The complexity of pseudo-Kronecker and free-Kronecker forms of functions over finite fields
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 3, pp. 285-299

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An approach enabling partial generalization of the Green–Sasao hierarchy for polynomial forms of Boolean functions to the case of an arbitrary finite field was introduced. The exact value of the Shannon function was obtained for the class of pseudo-Kroneker and free-Kronecker forms of $n$-ary functions over an arbitrary finite field $\mathbb F_q$. The value found is equal to $q^{n-1}$. The previously known result for Boolean functions was generalized.
Keywords: finite field, computational complexity, free-Kronecker forms, pseudo-Kronecker forms. 
@article{UZKU_2020_162_3_a3,
     author = {A. S. Baliuk},
     title = {The complexity of {pseudo-Kronecker} and {free-Kronecker} forms of functions over finite fields},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {285--299},
     publisher = {mathdoc},
     volume = {162},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2020_162_3_a3/}
}
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A. S. Baliuk. The complexity of pseudo-Kronecker and free-Kronecker forms of functions over finite fields. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 162 (2020) no. 3, pp. 285-299. http://geodesic.mathdoc.fr/item/UZKU_2020_162_3_a3/