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2022 Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes
András Pongrácz
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Publ. Mat. 66(1): 57-75 (2022). DOI: 10.5565/PUBLMAT6612202

Abstract

If S is the degree of a permutation group and s is the maximum degree of its elements, then S2s2. 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=2s3 and S=2s4.

Funding Statement

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 János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4 and ÚNKP-19-4 New National Excellence Programs of the Ministry of Human Capacities.

Funding Statement

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 János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4 and ÚNKP-19-4 New National Excellence Programs of the Ministry of Human Capacities.

Funding Statement

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 János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4 and ÚNKP-19-4 New National Excellence Programs of the Ministry of Human Capacities.

Citation

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András Pongrácz. "Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes." Publ. Mat. 66 (1) 57 - 75, 2022. https://doi.org/10.5565/PUBLMAT6612202

Information

Received: 7 January 2020; Accepted: 8 June 2021; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612202

Subjects:
Primary: 20B10 , 94B05 , 94B65

Keywords: anticode , code , maximum distance , Support

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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