Perfect mixed codes from generalized Reed-Muller codes Full article
| Journal |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
||
|---|---|---|---|
| Output data | Year: 2024, Volume: 92, Number: 1, Pages: 1-13 Pages count : 13 DOI: 10.1007/s10623-024-01364-3 | ||
| Tags | Mixed codes · Perfect codes · Quasi-perfect codes · Generalized Reed–Muller codes · MDS codes · Latin hypercubes | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0018 |
Abstract:
In this paper, we propose a new method for constructing 1-perfect mixed codes in the Cartesian product Fn × Fn q, where Fn and Fq are finite fields of orders n = qm and q. We consider generalized Reed-Muller codes of length n = qm and order (q − 1)m − 2. Codes whose parameters are the same as the parameters of generalized Reed-Muller codes are called Reed-Muller-like codes. The construction we propose is based on partitions of distance-2 MDS codes into Reed-Muller-like codes of order (q − 1)m − 2. We construct a set of qqcn nonequivalent 1-perfect mixed codes in the Cartesian product Fn ×Fn q , where the constant c satisfies c < 1, n = qm and m is a sufficiently large positive integer.We also prove that each 1-perfect mixed code in the Cartesian product Fn × Fn q corresponds to a certain partition of a distance-2 MDS code into Reed-Muller-like codes of order (q − 1)m − 2.
Cite:
Romanov A.M.
Perfect mixed codes from generalized Reed-Muller codes
Designs, Codes and Cryptography. 2024. V.92. N1. P.1-13. DOI: 10.1007/s10623-024-01364-3 WOS Scopus РИНЦ OpenAlex
Perfect mixed codes from generalized Reed-Muller codes
Designs, Codes and Cryptography. 2024. V.92. N1. P.1-13. DOI: 10.1007/s10623-024-01364-3 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | May 25, 2023 |
| Accepted: | Jan 18, 2024 |
| Published print: | Feb 5, 2024 |
| Published online: | Feb 5, 2024 |
Identifiers:
| Web of science: | WOS:001157688500003 |
| Scopus: | 2-s2.0-85184257842 |
| Elibrary: | 65973021 |
| OpenAlex: | W4391541503 |