An Approximation to Proof of the Circulant Hadamard Conjecture

2018/04/12 by Ronald Orozco López, López, Ronald Orozco · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1804.05007

openalex publication_date 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Turyn prove that if a circulant Hadamard matrix of order n exists then n must be of the form n=4m² for some odd integer m. In this paper we use the structure constant of Schur ring of \Z₂^4m² to prove that there is no circulant Hadamard matrix in \Z₂^4m² except possibly for sequences with Hamming weight a+b, with \fracm²-m2≤ a≤\frac3m²-m2 and b=2m²-m-a and with \fracm²+m2≤ 2m²-a≤\frac3m²+m2 and b=m+a.

Cited by

• Proof of the circulant Hadamard conjecture

Related

• Quadratic residues and a new infinity of orders for which a conjecture of Ryser about Circulant Hadamard matrices holds
• A proof of Ryser's circulant Hadamard conjecture
• A Note on Approximate Hadamard Matrices
• Ryser's Conjecture and Stochastic matrices
• A Real eigenvector of Circulant matrices and a conjecture of Ryser