Реферат: In Cayley graphs on the additive group of a small vector space over GF(q), q=2,3, we look for completely regular (CR) codes whose intersection array (IA) is new (see [2]) in Hamming graphs H(n,q) of the same degree (q 1)n over the same field. The existence of a CR code in such Cayley graph G implies the existence of a CR code with the same IA in the corresponding Hamming graph that covers G, see e.g. [3]. In such a way, we find several completely regular codes with new IA in Hamming graphs. The most interesting findings are two new CR-1 (with covering radius 1) codes that are independent sets (such CR are equivalent to optimal orthogonal arrays attaining the Bierbrauer–Friedman bound) and two new CR-2. By recursive constructions, every knew CR code induces an infinite sequence of CR codes (in particular, optimal orthogonal arrays if the original code is CR-1 and independent). In between, we classify feasible parameters of CR codes in several strongly regular graphs. New IAs {b;c} (for CR-1) and {b0,b1;c1,c2 } (for CR-2) in H(n, q) are shown in the table.

Библиографическая ссылка: Krotov D.
Completely regular codes in graphs covered by a Hamming graph
International Conference and PhD-Master Summer School "Groups and Graphs, Algebras and Applications" 04-17 Aug 2025