On q-ary shortened-1-perfect-like codes | Sciact - Система учета научной деятельности ИМ СО РАН

On q-ary shortened-1-perfect-like codes Научная публикация

Журнал

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

Вых. Данные

Год: 2022, Том: 68, DOI: 10.1109/TIT.2022.3187004

Ключевые слова

Binary codes; Codes; Hamming distance; Hamming graph; Mathematics; multifold packings; multiple coverings; perfect codes; Signal processing; Symbols; Upper bound

Авторы

Shi M. ¹ , Wu R. ² , Krotov D.S. ³

Организации

1	School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, Hefei, Anhui, China
2	School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China
3	Sobolev Institute of Mathematics

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0017

We study codes with parameters of q-ary shortened Hamming codes, i.e., (n=(q^m-q)/(q-1), q^{n-m}, 3)_q. Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such codes are optimal, generalizing it to a bound for multifold packings of radius-1 balls, with a corollary for multiple coverings. In particular, we show that the punctured Hamming code is an optimal q-fold packing with minimum distance 2. Secondly, for every admissible length starting from n = 20, we show the existence of 4-ary codes with parameters of shortened 1-perfect codes that cannot be obtained by shortening a 1-perfect code.

Shi M. , Wu R. , Krotov D.S.
On q-ary shortened-1-perfect-like codes
IEEE Transactions on Information Theory. 2022. V.68. DOI: 10.1109/TIT.2022.3187004 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	4 июл. 2021 г.
Принята к публикации:	22 июн. 2022 г.
Опубликована online:	12 июл. 2022 г.

Web of science:	WOS:000871032100012
Scopus:	2-s2.0-85134262861
РИНЦ:	57965139
OpenAlex:	W3205622575

БД	Цитирований
Scopus	2
Web of science	1
OpenAlex	2
РИНЦ	1