On $Z_p Z_{p^k}$ -Additive Codes and Their Duality Научная публикация
| Журнал |
IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
||||||
|---|---|---|---|---|---|---|---|
| Вых. Данные | Год: 2019, Том: 65, Номер: 6, Страницы: 3841-3847 Страниц : 7 DOI: 10.1109/tit.2018.2883759 | ||||||
| Ключевые слова | Dual codes, Gray map, linear codes, MacWilliams identity, two-weight codes, 1-perfect codes | ||||||
| Авторы |
|
||||||
| Организации |
|
Реферат:
In this paper, two different Gray-like maps from Zpα × Zpkβ, where p is prime, to Zpn , n=αtβpk-1 , denoted by φ and Φ, respectively, are presented. We have determined the connection between the weight enumerators among the image codes under these two mappings. We show that if C is a Zp Zpk-additive code, and C* is its dual, then the weight enumerators of the image p-ary codes φ(C) and Φ(C*) are formally dual. This is a partial generalization of [D. S. Krotov, On Z2k-dual binary codes, IEEE Transactions Information Theory 53 (2007), 1532-1537], and the result is generalized to odd characteristic p and mixed alphabet. In addition, a construction of 1-perfect additive codes in the mixed Zp Zp2 ... Zpk alphabet is given.
Библиографическая ссылка:
Shi M.
, Wu R.
, Krotov D.S.
On $Z_p Z_{p^k}$ -Additive Codes and Their Duality
IEEE Transactions on Information Theory. 2019. V.65. N6. P.3841-3847. DOI: 10.1109/tit.2018.2883759 WOS Scopus РИНЦ OpenAlex
On $Z_p Z_{p^k}$ -Additive Codes and Their Duality
IEEE Transactions on Information Theory. 2019. V.65. N6. P.3841-3847. DOI: 10.1109/tit.2018.2883759 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 23 авг. 2018 г. |
| Принята к публикации: | 22 нояб. 2018 г. |
| Опубликована online: | 30 нояб. 2018 г. |
Идентификаторы БД:
| Web of science: | WOS:000468433400032 |
| Scopus: | 2-s2.0-85057805645 |
| РИНЦ: | 41621162 |
| OpenAlex: | W2889940767 |