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

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings Full article

Journal

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

Output data

Year: 2023, Volume: 69, Number: 9, Article number : 3272566, Pages count : 7 DOI: 10.1109/TIT.2023.3272566

Tags

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

Authors

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

Affiliations

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

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

The Galois ring GR(4Delta) 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(4Delta) \{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(4Delta) and, if Delta is not a multiple of 3, under the action of the automorphism group of GR(4Delta). As a corollary, this implies the existence of quasi-cyclic additive 1-perfect codes of index (2Delta-1) in D((2Delta-1)(2Delta-2)/{6}, 2Delta-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

Submitted:	Apr 12, 2022
Accepted:	Apr 22, 2023
Published print:	Apr 27, 2023
Published online:	Apr 27, 2023

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

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Scopus	1