Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes
Pongrácz, András (University of Debrecen. Institute of Mathematics)

Data:	2022
Resum:	If S is the degree of a permutation group and s is the maximum degree of its elements, then S ≤ 2s − 2. We show that this inequality is sharp for some permutation group if and only if s is a power of 2, and then there is exactly one such permutation group up to isomorphism. The unique example is an elementary Abelian 2-group that arises from a punctured Hadamard code. Then we discuss the solutions of S = 2s − 3 and S = 2s − 4.
Nota:	This work is supported by the EFOP-3.6.2-16-2017-00015 and EFOP-3.6.1-16-2016-00022 projects, which have been supported by the European Union and are financed by the European Social Fund. The paper was also supported by the National Research, Development and Innovation Fund of Hungary, financed under the FK 124814 and PD 125160 funding schemes, the J'anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-18-4 and UNKP-19-4 New National Excellence Programs of the Ministry of Human Capacities.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Code ; Anticode ; Support ; Maximum distance
Publicat a:	Publicacions matemàtiques, Vol. 66 Núm. 1 (2022) , p. 57-75 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/396321
DOI: 10.5565/PUBLMAT6612202

19 p, 341.7 KB

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