Additive 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: 2019, Volume: 87, Number: 8, Pages: 1857-1869 Pages count : 13 DOI: 10.1007/s10623-018-0586-y | ||||
| Tags | distance regular graphs, additive perfect codes, Doob graphs, quasi-cyclic codes, tight 2-designs | ||||
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Abstract:
The Doob graph $D(m,n)$ is the Cartesian product of $m>0$ copies of the Shrikhande graph and $n$ copies of the complete graph of order $4$. Naturally, $D(m,n)$ can be represented as a Cayley graph on the additive group $(Z_4^2)^m \times (Z_2^2)^{n'} \times Z_4^{n''}$, where $n'+n''=n$. A set of vertices of $D(m,n)$ is called an additive code if it forms a subgroup of this group. We construct a $3$-parameter class of additive perfect codes in Doob graphs and show that the known necessary conditions of the existence of additive $1$-perfect codes in $D(m,n'+n'')$ are sufficient. Additionally, two quasi-cyclic additive $1$-perfect codes are constructed in $D(155,0+31)$ and $D(2667,0+127)$.
Cite:
Shi M.
, Huang D.
, Krotov D.S.
Additive perfect codes in Doob graphs
Designs, Codes and Cryptography. 2019. V.87. N8. P.1857-1869. DOI: 10.1007/s10623-018-0586-y WOS Scopus РИНЦ OpenAlex
Additive perfect codes in Doob graphs
Designs, Codes and Cryptography. 2019. V.87. N8. P.1857-1869. DOI: 10.1007/s10623-018-0586-y WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 7, 2018 |
| Accepted: | Nov 12, 2018 |
| Published online: | Nov 29, 2018 |
Identifiers:
| Web of science: | WOS:000472907800010 |
| Scopus: | 2-s2.0-85057841416 |
| Elibrary: | 41791226 |
| OpenAlex: | W3099948922 |