Codes from Layers of Hamming Graphs Научная публикация
| Конференция |
XIX International Symposium on Problems of Redundancy in Information and Control Systems 05-07 нояб. 2025 , Москва |
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| Сборник | XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy) Сборник, 2025. |
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| Вых. Данные | Год: 2025, Страницы: 1-5 Страниц : 5 DOI: 10.1109/redundancy68069.2025.11301429 | ||||
| Ключевые слова | codes from graphs, matrix rank, minimum distance problem, biregular parity check matrix, locally recoverable codes | ||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0017 |
Реферат:
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.
Библиографическая ссылка:
Danilko V.
, Mogilnykh I.
Codes from Layers of Hamming Graphs
В сборнике XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). 2025. – C.1-5. DOI: 10.1109/redundancy68069.2025.11301429 OpenAlex
Codes from Layers of Hamming Graphs
В сборнике XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy). 2025. – C.1-5. DOI: 10.1109/redundancy68069.2025.11301429 OpenAlex
Даты:
| Опубликована online: | 23 дек. 2025 г. |
Идентификаторы БД:
| OpenAlex: | W7116886765 |
Цитирование в БД:
Пока нет цитирований