Hadamard Matrices with Cocyclic Core

Víctor Álvarez, José Andrés Armario, María Dolores Frau, Félix Gudiel, María Belén Güemes and Amparo Osuna
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Víctor Álvarez: Department of Applied Mathematics I, University of Seville, 41004 Sevilla, Spain
José Andrés Armario: Department of Applied Mathematics I, University of Seville, 41004 Sevilla, Spain
María Dolores Frau: Department of Applied Mathematics I, University of Seville, 41004 Sevilla, Spain
Félix Gudiel: Department of Applied Mathematics I, University of Seville, 41004 Sevilla, Spain
María Belén Güemes: Department of Algebra, University of Seville, 41004 Sevilla, Spain
Amparo Osuna: Department of Applied Mathematics I, University of Seville, 41004 Sevilla, Spain

Mathematics, 2021, vol. 9, issue 8, 1-14

Abstract: Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.

Keywords: Hadamard matrix; circulant matrix; cocyclic matrix; difference set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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