Artículo
On Cocyclic Hadamard Matrices over Goethals-Seidel Loops
Autor/es | Álvarez Solano, Víctor
Armario Sampalo, José Andrés Falcón Ganfornina, Raúl Manuel Frau García, María Dolores Gudiel Rodríguez, Félix Güemes Alzaga, María Belén Osuna Lucena, Amparo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2020 |
Fecha de depósito | 2020-06-13 |
Publicado en |
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Resumen | About twenty-five years ago, Horadam and de Launey introduced the cocyclic development
of designs, from which the notion of cocyclic Hadamard matrices developed over a group was readily
derived. Much more recently, it ... About twenty-five years ago, Horadam and de Launey introduced the cocyclic development of designs, from which the notion of cocyclic Hadamard matrices developed over a group was readily derived. Much more recently, it has been proved that this notion may naturally be extended to define cocyclic Hadamard matrices developed over a loop. This paper delves into this last topic by introducing the concepts of coboundary, pseudocoboundary and pseudococycle over a quasigroup, and also the notion of the pseudococyclic Hadamard matrix. Furthermore, Goethals-Seidel loops are introduced as a family of Moufang loops so that every Hadamard matrix of Goethals-Seidel type (which is known not to be cocyclically developed over any group) is actually pseudococyclically developed over them. Finally, we also prove that, no matter if they are pseudococyclic matrices, the usual cocyclic Hadamard test is unexpectedly applicable. |
Agencias financiadoras | Junta de Andalucía |
Identificador del proyecto | FQM-016 |
Cita | Álvarez Solano, V., Armario Sampalo, J.A., Falcón Ganfornina, R.M., Frau García, M.D., Gudiel Rodríguez, F., Güemes Alzaga, M.B. y Osuna Lucena, A. (2020). On Cocyclic Hadamard Matrices over Goethals-Seidel Loops. Mathematics, 8 (1) |
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