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Codes from Layers of Hamming Graphs. / Danilko, Vitaly; Mogilnykh, Ivan.

2025. 1-5 Paper presented at 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy).

Research output: Contribution to conference › Paper › peer-review

Harvard

Danilko, V & Mogilnykh, I 2025, 'Codes from Layers of Hamming Graphs', Paper presented at 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 05.11.2025 - 07.11.2025 pp. 1-5. https://doi.org/10.1109/Redundancy68069.2025.11301429

APA

Danilko, V., & Mogilnykh, I. (2025). Codes from Layers of Hamming Graphs. 1-5. Paper presented at 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). https://doi.org/10.1109/Redundancy68069.2025.11301429

Vancouver

Danilko V, Mogilnykh I. Codes from Layers of Hamming Graphs. 2025. Paper presented at 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). doi: 10.1109/Redundancy68069.2025.11301429

Author

Danilko, Vitaly ; Mogilnykh, Ivan. / Codes from Layers of Hamming Graphs. Paper presented at 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy).5 p.

BibTeX

@conference{2da4bdd968444891b0f66cbbb0508f47,
title = "Codes from Layers of Hamming Graphs",
abstract = "We study the class of codes defined by the row space of the minimum distance relation matrix of t th and l th layers of Hamming graph H(m,q). By concatenating such matrices we obtain many distance-optimal codes of length up to 128. For arbitrary q,t,n,k we prove an analogue of a well-known Wilson rank formula [12] and find the dimensions of the codes in this class. For t=l−1, the codes are locally recoverable and include the codes from work of [11] for q=2. We show that the codes with q=2 are optimal locally-recoverable codes in our class.",
keywords = "коды на графах, ранг матрицы, задача минимального расстояния, бирегулярная проверочная матрица, локально восстанавливаемые коды, codes from graphs, matrix rank, minimum distance problem, biregular parity check matrix, locally recoverable codes",
author = "Vitaly Danilko and Ivan Mogilnykh",
note = "V. Danilko and I. Mogilnykh, {"}Codes from Layers of Hamming Graphs,{"} 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), Moscow, Russian Federation, 2025, pp. 1-5, doi: 10.1109/Redundancy68069.2025.11301429.; 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy) ; Conference date: 05-11-2025 Through 07-11-2025",
year = "2025",
month = nov,
day = "5",
doi = "10.1109/Redundancy68069.2025.11301429",
language = "English",
pages = "1--5",

}

RIS

TY - CONF

T1 - Codes from Layers of Hamming Graphs

AU - Danilko, Vitaly

AU - Mogilnykh, Ivan

N1 - V. Danilko and I. Mogilnykh, "Codes from Layers of Hamming Graphs," 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), Moscow, Russian Federation, 2025, pp. 1-5, doi: 10.1109/Redundancy68069.2025.11301429.

PY - 2025/11/5

Y1 - 2025/11/5

N2 - We study the class of codes defined by the row space of the minimum distance relation matrix of t th and l th layers of Hamming graph H(m,q). By concatenating such matrices we obtain many distance-optimal codes of length up to 128. For arbitrary q,t,n,k we prove an analogue of a well-known Wilson rank formula [12] and find the dimensions of the codes in this class. For t=l−1, the codes are locally recoverable and include the codes from work of [11] for q=2. We show that the codes with q=2 are optimal locally-recoverable codes in our class.

AB - We study the class of codes defined by the row space of the minimum distance relation matrix of t th and l th layers of Hamming graph H(m,q). By concatenating such matrices we obtain many distance-optimal codes of length up to 128. For arbitrary q,t,n,k we prove an analogue of a well-known Wilson rank formula [12] and find the dimensions of the codes in this class. For t=l−1, the codes are locally recoverable and include the codes from work of [11] for q=2. We show that the codes with q=2 are optimal locally-recoverable codes in our class.

KW - коды на графах

KW - ранг матрицы

KW - задача минимального расстояния

KW - бирегулярная проверочная матрица

KW - локально восстанавливаемые коды

KW - codes from graphs

KW - matrix rank

KW - minimum distance problem

KW - biregular parity check matrix

KW - locally recoverable codes

UR - https://www.scopus.com/pages/publications/105032114020

U2 - 10.1109/Redundancy68069.2025.11301429

DO - 10.1109/Redundancy68069.2025.11301429

M3 - Paper

SP - 1

EP - 5

T2 - 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy)

Y2 - 5 November 2025 through 7 November 2025

ER -

ID: 75601354