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Algebraic Design Theory and Hadamard Matrices pp 201–208Cite as

A Walsh–Fourier Approach to the Circulant Hadamard Conjecture

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 133))

Abstract

We describe an approach to the circulant Hadamard conjecture based on Walsh–Fourier analysis. We show that the existence of a circulant Hadamard matrix of order n is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.

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References

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Acknowledgements

The author was supported by OTKA grant No.​ 109789 and by ERC-AdG 321104.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 127, Budapest, 1364, Hungary

    Máté Matolcsi

Authors
  1. Máté Matolcsi
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Correspondence to Máté Matolcsi .

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Editors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona, USA

    Charles J. Colbourn

Additional information

Dedicated to Hadi Kharaghani on the occasion on his 70th birthday

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Matolcsi, M. (2015). A Walsh–Fourier Approach to the Circulant Hadamard Conjecture. In: Colbourn, C. (eds) Algebraic Design Theory and Hadamard Matrices. Springer Proceedings in Mathematics & Statistics, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-17729-8_16

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