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A proof of Ryser's circulant Hadamard conjecture

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arxiv 2302.08346 v1 pith:E6MB5YX3 submitted 2023-02-16 math.CO math.NT

Joshua Morris This is my paper · ORCID
classification math.COmath.NT
keywords circulantconjecturehadamardrysercongruenceequationsexistfamily
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abstract

We show that an $n\times n$ circulant Hadamard matrix must satisfy a family of congruence equations that have solutions only when $n \leq 4$, proving Ryser's 1963 conjecture that no such matrices exist for $n>4$.

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  1. Systematic Constructions of Complementary Sets and Hadamard Matrices from Circulant Operator

    eess.SP 2025-10 unverdicted novelty 7.0 of 10

    A claimed unified construction of CZCS/GCS/CCC/CZCSS and Hadamard matrices from circulant seeds is undermined by a false proof step and a counterexample in the paper's own example.

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