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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 5, Pages 1087–1100
DOI: https://doi.org/10.33048/smzh.2020.61.510
(Mi smj6039)
 

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

Combinatorial designs, difference sets, and bent functions as perfect colorings of graphs and multigraphs

V. N. Potapov, S. V. Avgustinovich

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (500 kB) Citations (5)
References:
Abstract: We prove that (1): the characteristic function of each independent set in each regular graph attaining the Delsarte–Hoffman bound is a perfect coloring; (2): each transversal in a uniform regular hypergraph is an independent set in the vertex adjacency multigraph of a hypergraph attaining the Delsarte–Hoffman bound for this multigraph; and (3): the combinatorial designs with parameters t-(v,k,λ) and their q-analogs, difference sets, Hadamard matrices, and bent functions are equivalent to perfect colorings of some graphs of multigraphs, in particular, the Johnson graph J(n,k) for (k1)-(v,k,λ)-designs and the Grassmann graph J2(n,2) for bent functions.
Keywords: perfect coloring, transversals of a hypergraph, combinatorial designs, q-analogs of combinatorial designs, difference sets, bent functions, Johnson graph, Grassmann graph, Delsarte–Hoffman bound.
Funding agency Grant number
Russian Science Foundation 18-11-00136
Siberian Branch of Russian Academy of Sciences I.5.1, проект № 0314-2019-0016
The first author was partly supported by the Russian Science Foundation (Grant 18–11–00136) (Sections 1–3). The second author was partly supported by the Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences I.5.1 (Project 0314–2019–0016) (Sections 4–6).
Received: 18.02.2020
Revised: 16.03.2020
Accepted: 08.04.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 5, Pages 867–877
DOI: https://doi.org/10.1134/S0037446620050109
Bibliographic databases:
Document Type: Article
UDC: 519.17+519.14
MSC: 35R30
Language: Russian
Citation: V. N. Potapov, S. V. Avgustinovich, “Combinatorial designs, difference sets, and bent functions as perfect colorings of graphs and multigraphs”, Sibirsk. Mat. Zh., 61:5 (2020), 1087–1100; Siberian Math. J., 61:5 (2020), 867–877
Citation in format AMSBIB
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  • This publication is cited in the following 5 articles:
    1. S. O. Borodin, A. A. Taranenko, “Perfect Colorings of Submatrix Hypergraphs”, J. Appl. Ind. Math., 18:3 (2024), 424  crossref
    2. A. A. Taranenko, “Perfect colourings of hypergraphs”, Linear and Multilinear Algebra, 2024, 1  crossref
    3. V. N. Potapov, “Upper bounds on the numbers of binary plateaued and bent functions”, Cryptogr. Commun., 2024  crossref
    4. Denis S. Krotov, 2023 XVIII International Symposium Problems of Redundancy in Information and Control Systems (REDUNDANCY), 2023, 82  crossref
    5. Vladimir N. Potapov, 2021 XVII International Symposium “Problems of Redundancy in Information and Control Systems” (REDUNDANCY), 2021, 95  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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