A. V. Menyachikhin, “Orthomorphisms of Abelian groups with minimum possible pairwise distances”, Diskr. Mat., 30:4 (2018), 55–65; Discrete Math. Appl., 30:3 (2020), 177

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Diskretnaya Matematika, 2018, Volume 30, Issue 4, Pages 55–65
DOI: https://doi.org/10.4213/dm1539 (Mi dm1539)

This article is cited in 5 scientific papers (total in 5 papers)

Orthomorphisms of Abelian groups with minimum possible pairwise distances

A. V. Menyachikhin

TVP Laboratories

Full-text PDF (185 kB) Citations (5)

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DOI: https://doi.org/10.4213/dm1539

Abstract: Orthomorphisms of Abelian groups with the minimum possible Cayley distance between them are studied. We describe the class of transformations mapping the given orthomorphism into the set of all orthomorphisms such that their Cayley distance from this orthomorphism takes the minimal possible value 2. Algorithms are suggested that construct all orthomorphisms separated from the given one by the minimum possible distance, and the complexity of these algorithms is estimated. Examples of Abelian groups are presented such that the set of all their orthomorphisms contains elements which are separated from all other orthomorphisms by a distance larger than the minimum possible.

Keywords: orthomorphism, Abelian group, Latin square, orthogonal Latin squares, Cayley distance, quasigroup,

$s$ -box, nonlinear transformation, permutation.

Received: 29.06.2018
Revised: 05.10.2018

English version:
Discrete Mathematics and Applications, 2020, Volume 30, Issue 3, Pages 177–186
DOI: https://doi.org/10.1515/dma-2020-0017

Bibliographic databases:

Document Type: Article

UDC: 512.541.5

Language: Russian

Citation: A. V. Menyachikhin, “Orthomorphisms of Abelian groups with minimum possible pairwise distances”, Diskr. Mat., 30:4 (2018), 55–65; Discrete Math. Appl., 30:3 (2020), 177–186

Citation in format AMSBIB

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\jour Discrete Math. Appl.

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Linking options:

https://www.mathnet.ru/eng/dm1539

https://doi.org/10.4213/dm1539

https://www.mathnet.ru/eng/dm/v30/i4/p55

This publication is cited in the following 5 articles:

O. A. Kozlitin, “Protokoly distantsionnogo golosovaniya. II”, Matem. vopr. kriptogr., 15:3 (2024), 83–100
S. V. Spiridonov, “Ortomorfizmy grupp s minimalno vozmozhnymi poparnymi rasstoyaniyami”, PDM, 2024, no. 66, 45–59
O. A. Kozlitin, M. A. Suleimanov, “Protokoly distantsionnogo golosovaniya. I”, Matem. vopr. kriptogr., 14:4 (2023), 89–110
R. A. de la Cruz Jiménez, “Constructing $8$ -bit permutations, $8$ -bit involutions and $8$ -bit orthomorphisms with almost optimal cryptographic parameters”, Matem. vopr. kriptogr., 12:3 (2021), 89–124
A. V. Menyachikhin, “The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups”, Discrete Math. Appl., 31:5 (2021), 327–343

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	1564
Full-text PDF :	118
References:	89
First page:	92

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