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

2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). Institute of Electrical and Electronics Engineers Inc., 2025. стр. 1-5.

Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование

Harvard

Danilko, V & Mogilnykh, I 2025, Codes from Layers of Hamming Graphs. в 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). Institute of Electrical and Electronics Engineers Inc., стр. 1-5, 2025 XIX International Symposium on Problems of Redundancy in Information and Control Systems, Москва, Российская Федерация, 05.11.2025. https://doi.org/10.1109/Redundancy68069.2025.11301429

APA

Danilko, V., & Mogilnykh, I. (2025). Codes from Layers of Hamming Graphs. в 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy) (стр. 1-5). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/Redundancy68069.2025.11301429

Vancouver

Danilko V, Mogilnykh I. Codes from Layers of Hamming Graphs. в 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). Institute of Electrical and Electronics Engineers Inc. 2025. стр. 1-5 doi: 10.1109/Redundancy68069.2025.11301429

Author

Danilko, Vitaly ; Mogilnykh, Ivan. / Codes from Layers of Hamming Graphs. 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). Institute of Electrical and Electronics Engineers Inc., 2025. стр. 1-5

BibTeX

@inproceedings{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. The work of the both authors was performed according to the Government research assignment for IM SB RAS, Project No. FWNF-2022-0017.; 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 = dec,
day = "23",
doi = "10.1109/Redundancy68069.2025.11301429",
language = "English",
isbn = "979-8-3315-4993-0",
pages = "1--5",
booktitle = "2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy)",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",

}

RIS

TY - GEN

T1 - Codes from Layers of Hamming Graphs

AU - Danilko, Vitaly

AU - Mogilnykh, Ivan

N1 - Conference code: 19

PY - 2025/12/23

Y1 - 2025/12/23

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 - Conference contribution

SN - 979-8-3315-4993-0

SP - 1

EP - 5

BT - 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy)

PB - Institute of Electrical and Electronics Engineers Inc.

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

Y2 - 5 November 2025 through 7 November 2025

ER -

ID: 75611112