The existence of perfect codes in Doob graphs Full article
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IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
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| Output data | Year: 2020, Volume: 66, Number: 3, Pages: 1423-1427 Pages count : 5 DOI: 10.1109/tit.2019.2946612 | ||
| Tags | Perfect codes, Doob graphs, Eisenstein-Jacobi integers | ||
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Abstract:
We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m, n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices.
Cite:
Krotov D.S.
The existence of perfect codes in Doob graphs
IEEE Transactions on Information Theory. 2020. V.66. N3. P.1423-1427. DOI: 10.1109/tit.2019.2946612 WOS Scopus РИНЦ OpenAlex
The existence of perfect codes in Doob graphs
IEEE Transactions on Information Theory. 2020. V.66. N3. P.1423-1427. DOI: 10.1109/tit.2019.2946612 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 8, 2018 |
| Accepted: | Aug 30, 2019 |
| Published online: | Oct 11, 2019 |
Identifiers:
| Web of science: | WOS:000519925900008 |
| Scopus: | 2-s2.0-85081054547 |
| Elibrary: | 43246952 |
| OpenAlex: | W3100822229 |