On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4 Научная публикация
| Журнал |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Вых. Данные | Год: 2008, Том: 308, Номер: 15, Страницы: 3322-3334 Страниц : 13 DOI: 10.1016/j.disc.2007.06.038 | ||
| Ключевые слова | MDS codes, n-ary quasigroups, Decomposability, Reducibility, Frequency hypercubes, Latin hypercubes | ||
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Реферат:
A subset S of {0, 1, ..., 2t-1}^n is called a t-fold MDS code if every line in each of n base directions contains exactly t elements of S. The adjacency graph of a t-fold MDS code is not connected if and only if the characteristic function of the code is the repetition-free sum of the characteristic functions of t-fold MDS codes of smaller lengths.
In the case t = 2, the theory has the following application. The union of two disjoint (n, 4^{n-1}), 2) MDS codes in {0, 1, 2, 3}^n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation as a test for reducibility of n-quasigroups of order 4. (C) 2007 Elsevier B.V. All rights reserved.
Библиографическая ссылка:
Krotov D.S.
On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4
Discrete Mathematics. 2008. V.308. N15. P.3322-3334. DOI: 10.1016/j.disc.2007.06.038 WOS Scopus РИНЦ OpenAlex
On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4
Discrete Mathematics. 2008. V.308. N15. P.3322-3334. DOI: 10.1016/j.disc.2007.06.038 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 4 нояб. 2005 г. |
| Принята к публикации: | 22 июн. 2007 г. |
| Опубликована online: | 7 авг. 2007 г. |
Идентификаторы БД:
| Web of science: | WOS:000257016500021 |
| Scopus: | 2-s2.0-43249091346 |
| РИНЦ: | 13579015 |
| OpenAlex: | W2022291866 |