On $Z_{2^k}$-Dual Binary Codes Научная публикация
| Журнал |
IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
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| Вых. Данные | Год: 2007, Том: 53, Номер: 4, Страницы: 1532-1537 Страниц : 6 DOI: 10.1109/tit.2007.892787 | ||
| Ключевые слова | Gray map, Hadamard codes, MacWilliams identity, perfect codes, $Z_{2^k}$-linearity | ||
| Авторы |
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| Организации |
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Реферат:
A new generalization of the Gray map is introduced. The new generalization $\Phi: Z_{2^k}^n \to Z_{2}^{2^{k-1}n}$ is connected with the known generalized Gray map $\varphi$ in the following way: if we take two dual linear $Z_{2^k}$-codes and construct binary codes from them using the generalizations $\varphi$ and $\Phi$ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The classes of $Z_{2^k}$-linear Hadamard codes and co-$Z_{2^k}$-linear extended 1-perfect codes are described, where co-$Z_{2^k}$-linearity means that the code can be obtained from a linear $Z_{2^k}$-code with the help of the new generalized Gray map.
Библиографическая ссылка:
Krotov D.S.
On $Z_{2^k}$-Dual Binary Codes
IEEE Transactions on Information Theory. 2007. V.53. N4. P.1532-1537. DOI: 10.1109/tit.2007.892787 WOS Scopus РИНЦ OpenAlex
On $Z_{2^k}$-Dual Binary Codes
IEEE Transactions on Information Theory. 2007. V.53. N4. P.1532-1537. DOI: 10.1109/tit.2007.892787 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 2 июл. 2006 г. |
| Опубликована online: | 26 мар. 2007 г. |
Идентификаторы БД:
| Web of science: | WOS:000245306000020 |
| Scopus: | 2-s2.0-34147161642 |
| РИНЦ: | 13544944 |
| OpenAlex: | W1987121126 |