Completely Regular Codes as Optimal Structures Научная публикация
| Конференция |
2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems 24-27 окт. 2023 , Москва, МИЭМ ВШЭ |
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| Сборник | 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY) Сборник, 2023. 204 c. |
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| Вых. Данные | Год: 2023, Страницы: 82 - 87 Страниц : 6 DOI: 10.1109/Redundancy59964.2023.10330185 | ||
| Ключевые слова | completely regular codes, intriguing sets, equitable partitions, optimal codes, diameter-perfect codes, orthogonal array, Bierbrauer–Friedman bound | ||
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Информация о финансировании (1)
| 1 | Российский научный фонд | 22-11-00266 |
Реферат:
We survey several results showing that optimal structures from different classes attaining a specific bound are described as completely regular codes with certain parameters. Examples of such structures are error-correcting codes, orthogonal arrays, edge cuts. We prove two new results of such kind. At first, we prove that in an arbitrary finite regular graph, an algebraic T-design attaining the Bierbrauer–Friedman–Potapov lower bound on its size is a completely regular code. (We recall that an algebraic T-design is a set of vertices of a graph whose characteristic function is orthogonal to all eigenfunctions corresponding to T largest non-main eigenvalues of the graph.) At second, we show that every diameter-perfect code is completely regular in a specially constructed graph. (We recall that a diameter-perfect code of distance d is a code C attaining the code-anticode bound |C| · |A| ≤ |S|, where S is the finite ambient metric space with transitive group of isometries and A, an anticode, is a set of diameter less than d).
Библиографическая ссылка:
Krotov D.S.
Completely Regular Codes as Optimal Structures
В сборнике 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY). 2023. – C.82 - 87. DOI: 10.1109/Redundancy59964.2023.10330185 Scopus OpenAlex
Completely Regular Codes as Optimal Structures
В сборнике 2023 XVIII International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY). 2023. – C.82 - 87. DOI: 10.1109/Redundancy59964.2023.10330185 Scopus OpenAlex
Даты:
| Опубликована в печати: | 4 дек. 2023 г. |
| Опубликована online: | 4 дек. 2023 г. |
Идентификаторы БД:
| Scopus: | 2-s2.0-85177770315 |
| OpenAlex: | W4389313749 |