A proof of Ryser's circulant Hadamard conjecture

2023/02/16 by Joshua Morris, Morris, Joshua · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.08346

openalex publication_date 2023/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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• Systematic Constructions of Complementary Sets and Hadamard Matrices from Circulant Operator

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