On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group Full article
| Journal |
Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253 |
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| Output data | Year: 2022, Volume: 58, Number: 1, Pages: 58-71 Pages count : 14 DOI: 10.1134/S0032946022010045 | ||
| Tags | affine group; perfect code; propelinear code; rank; regular action | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-21-00135 |
Abstract:
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.
Cite:
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
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
Original:
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
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
Identifiers:
| Web of science: | WOS:000780937000004 |
| Scopus: | 2-s2.0-85128235556 |
| Elibrary: | 48428746 |
| OpenAlex: | W4223527949 |