Abstract: We solve some first questions in the table of small parameters of completely regular (CR) codes in Hamming graphs H(n,q) . The most uplifting result is the existence of a {13,6,1;1,6,9}-CR code in H(n,2), n≥13. We also establish the non-existence of a {II,4;3,6}-code and a {10,3;4,7}-code in H(12,2) and H(13,2) . A partition of the complement of the quaternary Hamming code of length 5 into 4-cliques is found, which can be used to construct completely regular codes with covering radius 1 by known constructions. Additionally we discuss the parameters {24,21,10;1,4,12} of a putative completely regular code in H(24,2) and show the nonexistence of such a code in H(8,4) .

Cite: Krotov D.S.
On the existence of some completely regular codes in Hamming graphs
In compilation 2024 IEEE International Symposium on Information Theory (ISIT). – IEEE., 2024. – C.121-126. – ISBN 979-8-3503-8284-6. DOI: 10.1109/ISIT57864.2024.10619341 WOS Scopus OpenAlex

Dates:

Published print:	Aug 19, 2024
Published online:	Aug 19, 2024

Identifiers:

≡ Web of science:	WOS:001304426900020
≡ Scopus:	2-s2.0-85202864398
≡ OpenAlex:	W4401692924

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