Completely regular codes in graphs covered by a Hamming graph | Sciact - Система учета научной деятельности ИМ СО РАН

Completely regular codes in graphs covered by a Hamming graph Научная публикация

Журнал

Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586

Вых. Данные

Год: 2026, Том: 94, Номер статьи : 213, Страниц : 25 DOI: 10.1007/s10623-026-01955-2

Ключевые слова

completely regular codes, Hamming graphs, Cayley graphs, strongly regular graphs, graph covering, orthogonal arrays

Авторы

Goryainov S. ¹ , Krotov D. ²

Организации

1	School of Mathematical Sciences, Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Workstation for Foreign Academicians, Hebei Normal University, Shijiazhuang 050024, P.R. China
2	Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0011

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 parameters are new in Hamming graphs over the same field. The existence of a CR code in such a Cayley graph $G$ implies the existence of a CR code with the same parameters in the corresponding Hamming graph that covers $G$. In such a way, we find several completely regular codes with new parameters in Hamming graphs over GF$(2)$ and GF$(3)$. 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 one new CR-$2$ code. By recursive constructions, every new CR code induces an infinite sequence of CR codes (in particular, optimal orthogonal arrays if the original code is CR-$1$ and independent). Some of the found ternary CR codes disprove a conjectured generalization of the correlation-immunity bound on the strength of binary orthogonal arrays to the non-binary case. In between, we classify feasible parameters of CR codes in several strongly regular graphs.

Goryainov S. , Krotov D.
Completely regular codes in graphs covered by a Hamming graph
Designs, Codes and Cryptography. 2026. V.94. 213 :1-25. DOI: 10.1007/s10623-026-01955-2 Scopus OpenAlex

Поступила в редакцию:	30 апр. 2026 г.
Принята к публикации:	21 сент. 2026 г.
Опубликована в печати:	12 окт. 2026 г.
Опубликована online:	12 окт. 2026 г.

≡ Scopus:	2-s2.0-105053270721
≡ OpenAlex:	W4404451503