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Hadamard Matrices with Cocyclic Core

Author

Listed:
  • 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)

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.

Suggested Citation

  • Víctor Álvarez & José Andrés Armario & María Dolores Frau & Félix Gudiel & María Belén Güemes & Amparo Osuna, 2021. "Hadamard Matrices with Cocyclic Core," Mathematics, MDPI, vol. 9(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:857-:d:535930
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    Cited by:

    1. Shuhui Shen & Xiaojun Zhang, 2023. "Constructions of Goethals–Seidel Sequences by Using k -Partition," Mathematics, MDPI, vol. 11(2), pages 1-12, January.

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