Multifold 1‐perfect codes Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2024, Volume: 32, Number: 9, Pages: 546-555 Pages count : 11 DOI: 10.1002/jcd.21947 | ||
| Tags | additive codes, completely regular codes, intriguing sets, listdecoding codes, multifold packing, multiple covering, multispreads, perfect codes, spreads | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-11-00266 |
Abstract:
A multifold 1‐perfect code (1‐perfect code for list decoding) in any graph is a set C of vertices such that every vertex of the graph is at distance not more than 1 from exactly μ elements of C. In q‐ary Hamming graphs, where q is a prime power, we characterize all parameters of multifold 1‐perfect codes and all parameters of additive multifold 1‐perfect codes. In particular, we show that additive multifold 1‐perfect codes are related to special multiset generalizations of spreads, multispreads, and that multispreads of parameters corresponding to multifold 1‐perfect codes always exist.
Cite:
Krotov D.S.
Multifold 1‐perfect codes
Journal of Combinatorial Designs. 2024. V.32. N9. P.546-555. DOI: 10.1002/jcd.21947 WOS Scopus РИНЦ OpenAlex
Multifold 1‐perfect codes
Journal of Combinatorial Designs. 2024. V.32. N9. P.546-555. DOI: 10.1002/jcd.21947 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 10, 2022 |
| Published online: | May 20, 2024 |
| Published print: | Sep 16, 2024 |
Identifiers:
| Web of science: | WOS:001227463900001 |
| Scopus: | 2-s2.0-85193750365 |
| Elibrary: | 67604492 |
| OpenAlex: | W4398176024 |