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Mat. Sb., 2007, Volume 198, Number 7, Pages 31–44 (Mi msb1529)  

This article is cited in 1 scientific paper (total in 1 paper)

Splittability of $p$-ary functions

M. I. Anokhin

M. V. Lomonosov Moscow State University

Abstract: 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.

DOI: https://doi.org/10.4213/sm1529

Full text: PDF file (464 kB)
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English version:
Sbornik: Mathematics, 2007, 198:7, 935–947

Bibliographic databases:

UDC: 512.642+519.712.43
MSC: 15A03, 68Q17
Received: 14.02.2006 and 30.10.2006

Citation: M. I. Anokhin, “Splittability of $p$-ary functions”, Mat. Sb., 198:7 (2007), 31–44; Sb. Math., 198:7 (2007), 935–947

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1529
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. I. Anokhin, “Teoriya polnykh ortogonalnykh pryamykh razlozhenii vektornykh prostranstv”, PDM, 2012, no. 1(15), 11–49  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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