On extended 1-perfect bitrades Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Output data | Year: 2025, Volume: 348, Number: 1, Article number : 114222, Pages count : 12 DOI: 10.1016/j.disc.2024.114222 | ||
| Tags | Perfect code, Extended perfect code, Bitrade, Completely regular code, Uniformly packed code | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
| 2 | Russian Science Foundation | 18-11-00136 |
Abstract:
Extended 1-perfect codes in the Hamming scheme H(n, q) can be equivalently defined as codes that turn to 1-perfect codes after puncturing in any coordinate, as completely regular codes with certain intersection array, as uniformly packed codes with certain weight coefficients, as diameter perfect codes with respect to a certain anticode, as distance-4 codes with certain dual distances. We define extended 1-perfect bitrades in H(n, q) in f ive different manners, corresponding to the different definitions of extended 1-perfect codes, and prove the equivalence of these definitions of extended 1-perfect bitrades. For q=2m, we prove that such bitrades exist if and only if n =lq +2. For any q, we prove the nonexistence of extended 1-perfect bitrades if n is odd.
Cite:
Bespalov E.
, Krotov D.S.
On extended 1-perfect bitrades
Discrete Mathematics. 2025. V.348. N1. 114222 :1-12. DOI: 10.1016/j.disc.2024.114222 WOS Scopus РИНЦ OpenAlex
On extended 1-perfect bitrades
Discrete Mathematics. 2025. V.348. N1. 114222 :1-12. DOI: 10.1016/j.disc.2024.114222 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 14, 2023 |
| Accepted: | Aug 10, 2024 |
| Published print: | Aug 27, 2024 |
| Published online: | Aug 27, 2024 |
Identifiers:
| Web of science: | WOS:001303033500001 |
| Scopus: | 2-s2.0-85202048386 |
| Elibrary: | 80690514 |
| OpenAlex: | W3108899791 |
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