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On existence of perfect bitrades in Hamming graphs. / Mogilnykh, I. Yu; Solov'eva, F. I.

In: Discrete Mathematics, Vol. 343, No. 12, 112128, 12.2020.

Research output: Contribution to journal › Article › peer-review

Harvard

Mogilnykh, IY & Solov'eva, FI 2020, 'On existence of perfect bitrades in Hamming graphs', Discrete Mathematics, vol. 343, no. 12, 112128. https://doi.org/10.1016/j.disc.2020.112128

APA

Mogilnykh, I. Y., & Solov'eva, F. I. (2020). On existence of perfect bitrades in Hamming graphs. Discrete Mathematics, 343(12), [112128]. https://doi.org/10.1016/j.disc.2020.112128

Vancouver

Mogilnykh IY, Solov'eva FI. On existence of perfect bitrades in Hamming graphs. Discrete Mathematics. 2020 Dec;343(12):112128. doi: 10.1016/j.disc.2020.112128

Author

Mogilnykh, I. Yu ; Solov'eva, F. I. / On existence of perfect bitrades in Hamming graphs. In: Discrete Mathematics. 2020 ; Vol. 343, No. 12.

BibTeX

@article{85dd3f3d124746d0a04fb192c0412441,
title = "On existence of perfect bitrades in Hamming graphs",
abstract = "A pair (T0,T1) of disjoint sets of vertices of a graph G is called a perfect bitrade in G if any ball of radius 1 in G contains exactly one vertex in T0 and T1 or none simultaneously. The volume of a perfect bitrade (T0,T1) is the size of T0. If C0 and C1 are distinct perfect codes with minimum distance 3 in G then (C0∖C1,C1∖C0) is a perfect bitrade. For any q≥3, r≥1 we construct perfect bitrades of volume (q!)r in the Hamming graph H(qr+1,q) and show that for r=1 their volume is minimum.",
keywords = "Alternating group, MDS code, One-error-correcting code, Perfect bitrade, Perfect code, Spherical bitrade, MINIMUM SUPPORTS, CODES",
author = "Mogilnykh, {I. Yu} and Solov'eva, {F. I.}",
note = "Funding Information: This work was funded by the Russian Science Foundation under grant 18-11-00136. Publisher Copyright: {\textcopyright} 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = dec,
doi = "10.1016/j.disc.2020.112128",
language = "English",
volume = "343",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "12",

}

RIS

TY - JOUR

T1 - On existence of perfect bitrades in Hamming graphs

AU - Mogilnykh, I. Yu

AU - Solov'eva, F. I.

N1 - Funding Information: This work was funded by the Russian Science Foundation under grant 18-11-00136. Publisher Copyright: © 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - A pair (T0,T1) of disjoint sets of vertices of a graph G is called a perfect bitrade in G if any ball of radius 1 in G contains exactly one vertex in T0 and T1 or none simultaneously. The volume of a perfect bitrade (T0,T1) is the size of T0. If C0 and C1 are distinct perfect codes with minimum distance 3 in G then (C0∖C1,C1∖C0) is a perfect bitrade. For any q≥3, r≥1 we construct perfect bitrades of volume (q!)r in the Hamming graph H(qr+1,q) and show that for r=1 their volume is minimum.

AB - A pair (T0,T1) of disjoint sets of vertices of a graph G is called a perfect bitrade in G if any ball of radius 1 in G contains exactly one vertex in T0 and T1 or none simultaneously. The volume of a perfect bitrade (T0,T1) is the size of T0. If C0 and C1 are distinct perfect codes with minimum distance 3 in G then (C0∖C1,C1∖C0) is a perfect bitrade. For any q≥3, r≥1 we construct perfect bitrades of volume (q!)r in the Hamming graph H(qr+1,q) and show that for r=1 their volume is minimum.

KW - Alternating group

KW - MDS code

KW - One-error-correcting code

KW - Perfect bitrade

KW - Perfect code

KW - Spherical bitrade

KW - MINIMUM SUPPORTS

KW - CODES

UR - http://www.scopus.com/inward/record.url?scp=85090039781&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2020.112128

DO - 10.1016/j.disc.2020.112128

M3 - Article

AN - SCOPUS:85090039781

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

M1 - 112128

ER -

ID: 26029676