On Perfect and Reed–Muller Codes over Finite Fields Научная публикация
| Журнал |
Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253 |
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| Вых. Данные | Год: 2021, Том: 57, Номер: 3, Страницы: 199-211 Страниц : 13 DOI: 10.1134/S0032946021030017 | ||
| Ключевые слова | affine Reed–Muller code; finite field; Hamming code; MDS code; perfect code; projective Reed–Muller code; quasi-perfect code; Reed–Muller code | ||
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Реферат:
We consider error-correcting codes over a finite field with q elements (q-ary codes). We study relations between single-error-correcting q-ary perfect codes and q-ary Reed–Muller codes. For q we find parameters of affine Reed–Muller codes of order (q-1)m-2. We show that affine Reed–Muller codes of order (q-1)m-2 are quasi-perfect codes. We propose a construction which allows to construct single-error-correcting q-ary perfect codes from codes with parameters of affine Reed–Muller codes. A modification of this construction allows to construct q-ary quasi-perfect codes with parameters of affine Reed–Muller codes. © 2021, Pleiades Publishing, Inc.
Библиографическая ссылка:
Romanov A.M.
On Perfect and Reed–Muller Codes over Finite Fields
Problems of Information Transmission. 2021. V.57. N3. P.199-211. DOI: 10.1134/S0032946021030017 WOS Scopus OpenAlex
On Perfect and Reed–Muller Codes over Finite Fields
Problems of Information Transmission. 2021. V.57. N3. P.199-211. DOI: 10.1134/S0032946021030017 WOS Scopus OpenAlex
Идентификаторы БД:
| Web of science: | WOS:000704980200001 |
| Scopus: | 2-s2.0-85116527970 |
| OpenAlex: | W3203516005 |