Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings | Sciact - Система учета научной деятельности ИМ СО РАН

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings Научная публикация

Журнал

IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654

Вых. Данные

Год: 2023, Том: 69, Номер: 9, Номер статьи : 3272566, Страниц : 7 DOI: 10.1109/TIT.2023.3272566

Ключевые слова

Doob graph, Galois ring, 1-perfect code, quasicyclic code

Авторы

Shi M. ¹ , Li X. ¹ , Krotov D.S. ² , Özbudak F. ^3,4

Организации

1	Key Laboratory of Intelligent Computing and Signal Processing, School of Mathematical Sciences, Ministry of Education, Anhui University
2	State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences
3	Faculty of Engineering and Natural Sciences, Sabancı University, 34956, Istanbul
4	D.M., Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0017

The Galois ring GR$(4^\Delta)$ is the residue ring $Z_4[x]/(h(x))$, where $h(x)$ is a basic primitive polynomial of degree $\Delta$ over $Z_4$. For any odd $\Delta$ larger than $1$, we construct a partition of GR$(4^\Delta) \backslash \{0\}$ into $6$-subsets of type $\{a,b,-a-b,-a,-b,a+b\}$ and $3$-subsets of type $\{c,-c,2c\}$ such that the partition is invariant under the multiplication by a nonzero element of the Teichmuller set in GR$(4^\Delta)$ and, if $\Delta$ is not a multiple of $3$, under the action of the automorphism group of GR$(4^\Delta)$. As a corollary, this implies the existence of quasi-cyclic additive $1$-perfect codes of index $(2^\Delta-1)$ in $D((2^\Delta-1)(2^\Delta-2)/{6}, 2^\Delta-1 )$ where $D(m,n)$ is the Doob metric scheme on $Z^{2m+n}$.

Shi M. , Li X. , Krotov D.S. , Özbudak F.
Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings
IEEE Transactions on Information Theory. 2023. V.69. N9. 3272566 :1-7. DOI: 10.1109/TIT.2023.3272566 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	12 апр. 2022 г.
Принята к публикации:	22 апр. 2023 г.
Опубликована в печати:	27 апр. 2023 г.
Опубликована online:	27 апр. 2023 г.

Web of science:	WOS:001064724800006
Scopus:	2-s2.0-85159840820
РИНЦ:	64379700
OpenAlex:	W4368232606

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