Some completely regular codes in Doob graphs Full article
| Source | Completely Regular Codes in Distance-Regular Graphs Monography, Chapman & Hall. 2025. 504 c. ISBN 9781032494449. Scopus |
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| Output data | Year: 2025, Number: Chapter 6, Pages: 379-448 Pages count : 70 DOI: 10.1201/9781003393931-6 | ||
| Tags | Doob graph; Shrikhande graph; completely regular code; equitable partition; perfect code; linear code; additive code; extended perfect code; MDS code | ||
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Funding (3)
| 1 | Russian Science Foundation | 22-11-00266 |
| 2 | Russian Science Foundation | 18-11-00136 |
| 3 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
The Doob graph on 4^n vertices is a distance regular graph with the same parameters as the Hamming graphs $H(n,4)$ but non isomorphic to it. It can be constructed by taking the Cartesian product of $m>0$ copies of the Shrikhande graph, a special strongly regular graph on 16 vertices, and $n-2m$ copies of the Hamming graph $H(1,4)$. For Doob graphs, we prove MacWilliams-type theorems connecting the weight distributions of dual additive codes, describe the characterization of parameters of perfect codes, multifold perfect codes, and extended perfect codes and the characterization of maximum distance-separable codes (including a characterization of such codes in Hamming graphs $H(n,4)$), and obtain a sequence of results on admissibility of intersection arrays of completely regular codes with covering radius $1$.
Cite:
Bespalov E.A.
, Krotov D.S.
Some completely regular codes in Doob graphs
Monography chapter Completely Regular Codes in Distance-Regular Graphs. – Chapman & Hall., 2025. – C.379-448. – ISBN 9781032494449. DOI: 10.1201/9781003393931-6 Scopus OpenAlex
Some completely regular codes in Doob graphs
Monography chapter Completely Regular Codes in Distance-Regular Graphs. – Chapman & Hall., 2025. – C.379-448. – ISBN 9781032494449. DOI: 10.1201/9781003393931-6 Scopus OpenAlex
Dates:
| Published online: | Mar 15, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105001331744 |
| OpenAlex: | W4407438298 |
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