Splittability of $p$-ary functions

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.
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