Splittability of $p$-ary functions
Sbornik. Mathematics, Tome 198 (2007) no. 7, pp. 935-947
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A function $\varphi$ from an $n$-dimensional vector space $V$ over
a field $F$ of $p$ elements (where $p$ is a prime) into $F$
is called splittable if
$\varphi(u+w)=\psi(u)+\chi(w)$, $u\in U$,
$w\in W$, for some non-trivial subspaces $U$ and $W$
such that $U\oplus W=V$ and for some functions $\psi\colon U\to F$ and
$\chi\colon W\to F$. It is explained how one can verify in time polynomial
in
$\log p^{p^n}$ whether a function is splittable and, if it is,
find a representation of it in the above-described form. Other
questions relating to the splittability of functions are considered.
Bibliography: 3 titles.
@article{SM_2007_198_7_a1,
author = {M. I. Anokhin},
title = {Splittability of $p$-ary functions},
journal = {Sbornik. Mathematics},
pages = {935--947},
publisher = {mathdoc},
volume = {198},
number = {7},
year = {2007},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2007_198_7_a1/}
}
M. I. Anokhin. Splittability of $p$-ary functions. Sbornik. Mathematics, Tome 198 (2007) no. 7, pp. 935-947. http://geodesic.mathdoc.fr/item/SM_2007_198_7_a1/