An enumeration of 1-perfect ternary codes Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Output data | Year: 2023, Volume: 346, Number: 7, Article number : 113437, Pages count : 16 DOI: 10.1016/j.disc.2023.113437 | ||||||
| Tags | Perfect codes, Ternary codes, Concatenation, Switching | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
We study codes with parameters of the ternary Hamming $(n=(3^m-1)/2, 3^{n-m}, 3)$ code, i.e., ternary 1-perfect codes. The rank of the code is defined to be the dimension of its affine span. We characterize ternary 1-perfect codes of rank n-m+1, count their number, and prove that all such codes can be obtained from each other by a sequence of two-coordinate switchings. We enumerate ternary 1-perfect codes of length 13 obtained by concatenation from codes of lengths 9 and 4; we find that there are 93241327 equivalence classes of such codes.
Cite:
Shi M.
, Krotov D.S.
An enumeration of 1-perfect ternary codes
Discrete Mathematics. 2023. V.346. N7. 113437 :1-16. DOI: 10.1016/j.disc.2023.113437 WOS Scopus РИНЦ OpenAlex
An enumeration of 1-perfect ternary codes
Discrete Mathematics. 2023. V.346. N7. 113437 :1-16. DOI: 10.1016/j.disc.2023.113437 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 15, 2022 |
| Accepted: | Mar 22, 2023 |
| Published print: | Apr 4, 2023 |
| Published online: | Apr 4, 2023 |
Identifiers:
| Web of science: | WOS:000978319500001 |
| Scopus: | 2-s2.0-85151510745 |
| Elibrary: | 61981255 |
| OpenAlex: | W4362635821 |