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Matematicheskie Trudy, 2011, Volume 14, Number 2, Pages 147–172 (Mi mt219)  
This article is cited in 9 scientific papers (total in 9 papers)

On extensions of partial $n$-quasigroups of order 4

V. N. Potapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (314 kB) Citations (9)
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Abstract: We prove that every collection of pairwise compatible (nowhere coinciding) $n$-ary quasigroups of order 4 can be extended to an $(n+1)$-ary quasigroup. In other words, every Latin $4\times\cdots\times4\times l$-parallelepiped, where $l=1,2,3$, can be extended to a Latin hypercube.
Key words: $n$-ary quasigroup, reducible $n$-quasigroup, semilinear $n$-quasigroup of order 4, Latin $n$-cube, MDS-code.
Received: 24.09.2010
English version:
Siberian Advances in Mathematics, 2012, Volume 22, Issue 2, Pages 135–151
DOI: https://doi.org/10.3103/S1055134412020058
Bibliographic databases:
Document Type: Article
UDC: 519.143
Language: Russian
Citation: V. N. Potapov, “On extensions of partial $n$-quasigroups of order 4”, Mat. Tr., 14:2 (2011), 147–172; Siberian Adv. Math., 22:2 (2012), 135–151
Citation in format AMSBIB
\Bibitem{Pot11}
\by V.~N.~Potapov
\paper On extensions of partial $n$-quasigroups of order~4
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 2
\pages 147--172
\mathnet{http://mi.mathnet.ru/mt219}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2961772}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 2
\pages 135--151
\crossref{https://doi.org/10.3103/S1055134412020058}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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