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Some remarks on Hadamard matrices

Journal Article


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Abstract


  • In this note we use combinatorial methods to show that the unique, up to

    equivalence, 5 × 5 (1,−1)-matrix with determinant 48, the unique, up to equivalence,

    6 × 6 (1,−1)-matrix with determinant 160, and the unique, up to equivalence, 7 × 7

    (1,−1)-matrix with determinant 576, all cannot be embedded in the Hadamard

    matrix of order 8. We also review some properties of Sylvester Hadamard matrices,

    their Smith Normal Forms, and pivot patterns of Hadamard matrices when Gaussian

    Elimination with complete pivoting is applied on them. The pivot values which

    appear reconfirm the above non-embedding results.

Publication Date


  • 2010

Citation


  • Seberry, J. & Mitrouli, M. (2010). Some remarks on Hadamard matrices. Cryptography and Communications-Discrete Structures, Boolean Functions and Sequences, 2 (2), 293-306.

Scopus Eid


  • 2-s2.0-84859759485

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1869&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/852

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 293

End Page


  • 306

Volume


  • 2

Issue


  • 2

Abstract


  • In this note we use combinatorial methods to show that the unique, up to

    equivalence, 5 × 5 (1,−1)-matrix with determinant 48, the unique, up to equivalence,

    6 × 6 (1,−1)-matrix with determinant 160, and the unique, up to equivalence, 7 × 7

    (1,−1)-matrix with determinant 576, all cannot be embedded in the Hadamard

    matrix of order 8. We also review some properties of Sylvester Hadamard matrices,

    their Smith Normal Forms, and pivot patterns of Hadamard matrices when Gaussian

    Elimination with complete pivoting is applied on them. The pivot values which

    appear reconfirm the above non-embedding results.

Publication Date


  • 2010

Citation


  • Seberry, J. & Mitrouli, M. (2010). Some remarks on Hadamard matrices. Cryptography and Communications-Discrete Structures, Boolean Functions and Sequences, 2 (2), 293-306.

Scopus Eid


  • 2-s2.0-84859759485

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1869&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/852

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 293

End Page


  • 306

Volume


  • 2

Issue


  • 2