Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes

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András Pongrácz
University of Debrecen. Institute of Mathematics
https://orcid.org/0000-0002-2771-8974

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

Keywords
code, anticode, support, maximum distance

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How to Cite
Pongrácz, András. “Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes”. Publicacions Matemàtiques, 2022, vol.VOL 66, no. 1, pp. 57-75, https://raco.cat/index.php/PublicacionsMatematiques/article/view/396321.
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