Some completely regular codes in Doob graphs | Sciact - Система учета научной деятельности ИМ СО РАН

Some completely regular codes in Doob graphs Научная публикация

Сборник

Completely Regular Codes in Distance-Regular Graphs
Монография, Chapman & Hall. 2025. 504 c. ISBN 9781032494449. Scopus

Вых. Данные

Год: 2025, Номер: Chapter 6, Страницы: 379-448 Страниц : 70 DOI: 10.1201/9781003393931-6

Ключевые слова

Doob graph; Shrikhande graph; completely regular code; equitable partition; perfect code; linear code; additive code; extended perfect code; MDS code

Авторы

Bespalov Evgeny A. ¹ , Krotov Denis S. ¹

Организации

1	Sobolev Institute of Mathematics

Информация о финансировании (3)

1	Российский научный фонд	22-11-00266
2	Российский научный фонд	18-11-00136
3	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0017

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 $1$.

Bespalov E.A. , Krotov D.S.
Some completely regular codes in Doob graphs
Глава монографии Completely Regular Codes in Distance-Regular Graphs. – Chapman & Hall., 2025. – C.379-448. – ISBN 9781032494449. DOI: 10.1201/9781003393931-6 Scopus OpenAlex

Опубликована online:

15 мар. 2025 г.

Scopus:	2-s2.0-105001331744
OpenAlex:	W4407438298

Пока нет цитирований