Geodesic
Upper bound for the length of functions over a finite field in the class of pseudopolynomials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 899-904

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

An exclusive-OR sum of pseudoproducts (ESPP), or a pseudopolynomial over a finite field is a sum of products of linear functions. The length of an ESPP is defined as the number of its pairwise distinct summands. The length of a function $f$ over this field in the class of ESPPs is the minimum length of an ESPP representing this function. The Shannon length function $L_k^{\text{ESPP}}(n)$ on the set of functions over a finite field of $k$ elements in the class of ESPPs is considered; it is defined as the maximum length of a function of n variables over this field in the class of ESPPs. It is proved that $L_k^{\text{ESPP}}(n)=O(k^n/n^2)$. 
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     title = {Upper bound for the length of functions over a finite field in the class of pseudopolynomials},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {57},
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S. N. Selezneva. Upper bound for the length of functions over a finite field in the class of pseudopolynomials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 899-904. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a12/