Perfect mixed codes from generalized Reed-Muller codes Научная публикация
| Журнал |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Вых. Данные | Год: 2024, Том: 92, Номер: 1, Страницы: 1-13 Страниц : 13 DOI: 10.1007/s10623-024-01364-3 | ||
| Ключевые слова | Mixed codes · Perfect codes · Quasi-perfect codes · Generalized Reed–Muller codes · MDS codes · Latin hypercubes | ||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0018 |
Реферат:
In this paper, we propose a new method for constructing 1-perfect mixed codes in the Cartesian product Fn × Fn q, where Fn and Fq are finite fields of orders n = qm and q. We consider generalized Reed-Muller codes of length n = qm and order (q − 1)m − 2. Codes whose parameters are the same as the parameters of generalized Reed-Muller codes are called Reed-Muller-like codes. The construction we propose is based on partitions of distance-2 MDS codes into Reed-Muller-like codes of order (q − 1)m − 2. We construct a set of qqcn nonequivalent 1-perfect mixed codes in the Cartesian product Fn ×Fn q , where the constant c satisfies c < 1, n = qm and m is a sufficiently large positive integer.We also prove that each 1-perfect mixed code in the Cartesian product Fn × Fn q corresponds to a certain partition of a distance-2 MDS code into Reed-Muller-like codes of order (q − 1)m − 2.
Библиографическая ссылка:
Romanov A.M.
Perfect mixed codes from generalized Reed-Muller codes
Designs, Codes and Cryptography. 2024. V.92. N1. P.1-13. DOI: 10.1007/s10623-024-01364-3 WOS Scopus РИНЦ OpenAlex
Perfect mixed codes from generalized Reed-Muller codes
Designs, Codes and Cryptography. 2024. V.92. N1. P.1-13. DOI: 10.1007/s10623-024-01364-3 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 25 мая 2023 г. |
| Принята к публикации: | 18 янв. 2024 г. |
| Опубликована в печати: | 5 февр. 2024 г. |
| Опубликована online: | 5 февр. 2024 г. |
Идентификаторы БД:
| Web of science: | WOS:001157688500003 |
| Scopus: | 2-s2.0-85184257842 |
| РИНЦ: | 65973021 |
| OpenAlex: | W4391541503 |