Perfect codes in Doob graphs Full article
| Journal |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Output data | Year: 2016, Volume: 80, Number: 1, Pages: 91-102 Pages count : 12 DOI: 10.1007/s10623-015-0066-6 | ||||
| Tags | Perfect codes, Doob graphs, Distance regular graphs | ||||
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Abstract:
We study 1-perfect codes in Doob graphs D(m,n). We show that such codes that are linear over the Galois ring GR(4^2) exist if and only if there exist integers γ≥0 and δ>0 such that n=(4^{γ+δ}-1)/3 and m=(4^{γ+2δ}-4^{γ+δ})/6. We also prove necessary conditions on (m,n) for 1-perfect codes that are linear over Z4 (we call such codes additive) to exist in D(m,n) graphs; for some of these parameters, we show the existence of codes. For every m and n satisfying 2m+n=(4^μ-1)/3 and m≤(4^μ-5⋅2^{μ-1}+1)/9, we construct 1-perfect codes in D(m,n), which do not necessarily have a group structure.
Cite:
Krotov D.S.
Perfect codes in Doob graphs
Designs, Codes and Cryptography. 2016. V.80. N1. P.91-102. DOI: 10.1007/s10623-015-0066-6 WOS Scopus РИНЦ OpenAlex
Perfect codes in Doob graphs
Designs, Codes and Cryptography. 2016. V.80. N1. P.91-102. DOI: 10.1007/s10623-015-0066-6 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 21, 2014 |
| Accepted: | Mar 13, 2015 |
| Published online: | Mar 26, 2015 |
Identifiers:
| Web of science: | WOS:000377188000006 |
| Scopus: | 2-s2.0-84925638625 |
| Elibrary: | 26753000 |
| OpenAlex: | W3102043406 |