On Perfect and Reed–Muller Codes over Finite Fields Full article
| Journal |
Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253 |
||
|---|---|---|---|
| Output data | Year: 2021, Volume: 57, Number: 3, Pages: 199-211 Pages count : 13 DOI: 10.1134/S0032946021030017 | ||
| Tags | affine Reed–Muller code; finite field; Hamming code; MDS code; perfect code; projective Reed–Muller code; quasi-perfect code; Reed–Muller code | ||
| Authors |
|
||
| Affiliations |
|
Abstract:
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.
Cite:
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
Identifiers:
| Web of science: | WOS:000704980200001 |
| Scopus: | 2-s2.0-85116527970 |
| OpenAlex: | W3203516005 |