On the structure of non-full-rank perfect q-ary codes Научная публикация
| Журнал |
Advances in Mathematics of Communications
ISSN: 1930-5346 , E-ISSN: 1930-5338 |
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| Вых. Данные | Год: 2011, Том: 5, Номер: 2, Страницы: 149-156 Страниц : 8 DOI: 10.3934/amc.2011.5.149 | ||||||
| Ключевые слова | lower bound, q-ary codes, perfect codes, components | ||||||
| Авторы |
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Реферат:
The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the q-ary case. Simply speaking, every non-full-rank perfect code C is the union of a well-defined family of (mu) over bar -components K_\mu, where \mu over bar belongs to an "outer" perfect code C', and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain \mu-components, and new lower bounds on the number of perfect 1-error-correcting q-ary codes are presented.
Библиографическая ссылка:
Heden O.
, Krotov D.S.
On the structure of non-full-rank perfect q-ary codes
Advances in Mathematics of Communications. 2011. V.5. N2. P.149-156. DOI: 10.3934/amc.2011.5.149 WOS Scopus РИНЦ OpenAlex
On the structure of non-full-rank perfect q-ary codes
Advances in Mathematics of Communications. 2011. V.5. N2. P.149-156. DOI: 10.3934/amc.2011.5.149 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 31 мар. 2010 г. |
| Принята к публикации: | 31 авг. 2010 г. |
Идентификаторы БД:
| Web of science: | WOS:000293562800002 |
| Scopus: | 2-s2.0-79955752862 |
| РИНЦ: | 16991923 |
| OpenAlex: | W1525308658 |