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2014•arXiv (Cornell University)Open access

A Walsh-Fourier approach to the circulant Hadamard conjecture

Máté Matolcsi

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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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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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Available 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.

Key concepts: Hadamard three-lines theorem, Hadamard transform, Circulant matrix, Hadamard three-circle theorem, Hadamard matrix, Conjecture, Hadamard's inequality, Complex Hadamard matrix

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