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

• Autores: András Pongrácz
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 66, Nº 1, 2022, págs. 57-75
• Idioma: catalán
• Títulos paralelos:
  • Extremal solutions of an inequality concerning supports of permutation groups and punctured Hadamard codes
• Enlaces
  • Texto completo
• Resumen

  • 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