On non-full-rank perfect codes over finite fields Научная публикация
| Журнал |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Вых. Данные | Год: 2019, Том: 87, Номер: 5, Страницы: 995-1003 Страниц : 9 DOI: 10.1007/s10623-018-0506-1 | ||
| Ключевые слова | Concatenation; Hamming code; MDS code; Perfect code; Rank | ||
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Реферат:
The paper deals with perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to a q-ary non-full-rank 1-perfect code of length n= (q m - 1) / (q- 1) is a q-ary constant-weight code with Hamming weight equal to q m - 1 , where m is any natural number not less than two. Necessary and sufficient conditions for q-ary codes to be q-ary non-full-rank 1-perfect codes are obtained. We suggest a generalization of the concatenation construction to the q-ary case and construct a ternary 1-perfect code of length 13 and rank 12. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Библиографическая ссылка:
Romanov A.M.
On non-full-rank perfect codes over finite fields
Designs, Codes and Cryptography. 2019. V.87. N5. P.995-1003. DOI: 10.1007/s10623-018-0506-1 WOS Scopus OpenAlex
On non-full-rank perfect codes over finite fields
Designs, Codes and Cryptography. 2019. V.87. N5. P.995-1003. DOI: 10.1007/s10623-018-0506-1 WOS Scopus OpenAlex
Идентификаторы БД:
| Web of science: | WOS:000465452000005 |
| Scopus: | 2-s2.0-85048140792 |
| OpenAlex: | W2247110676 |