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On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group Научная публикация

Журнал

Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253

Вых. Данные

Год: 2022, Том: 58, Номер: 1, Страницы: 58-71 Страниц : 14 DOI: 10.1134/S0032946022010045

Ключевые слова

affine group; perfect code; propelinear code; rank; regular action

Авторы

Mogilnykh I.Y. ¹

Организации

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation

Информация о финансировании (1)

Российский научный фонд

22-21-00135

A code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group Ga(R,Q) of affine transformations is said to be regular if it acts regularly on vectors of Fqr. Every automorphism of a regular subgroup of the general affine group GA(r, q) induces a permutation on the cosets of the Hamming code of length (Formula presented.). Based on this permutation, we propose a construction of q-ary propelinear perfect codes of length (Formula presented.). In particular, for any prime q we obtain an infinite series of almost full rank q-ary propelinear perfect codes. © 2022, Pleiades Publishing, Inc.

Mogilnykh I.Y.
On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group
Problems of Information Transmission. 2022. V.58. N1. P.58-71. DOI: 10.1134/S0032946022010045 WOS Scopus РИНЦ OpenAlex

Могильных И.Ю.
О $q$-ичных пропелинейных совершенных кодах на основе регулярных подгрупп общей аффинной группы
Проблемы передачи информации. 2022. Т.58. №1. С.65-79. DOI: 10.31857/S0555292322010041 РИНЦ OpenAlex

Web of science:	WOS:000780937000004
Scopus:	2-s2.0-85128235556
РИНЦ:	48428746
OpenAlex:	W4223527949

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