Реферат: 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 {11, 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).

Библиографическая ссылка: Krotov D.S.
On the existence of some completely regular codes in Hamming graphs
2024 IEEE International Symposium on Information Theory 7 Jul - 12 Aug 2024