Construction of Regular Hadamard Matrices From Circulant Hadamard Matrices and Ryser’s Conjecture - Manjhi, Pankaj Kumar; Kumar, Jitendra (Communications in Mathematics and Applications, 2025)
This article presents a simplified proof of Ryser’s conjecture by building upon and extending the modular arithmetic framework introduced by Luis Henri Gallardo (On Ryser’s conjecture: modulo 2 approach, Applied Mathematics E-Notes 21 (2021), 220 – 224,), specifically leveraging the modulo 2 approach. The methodology highlights an accessible and robust pathway to understanding the conjecture’s constraints, providing new insights into the structural properties of circulant and regular Hadamard matrices.
Keywords: Hadamard matrix; Partial Hadamard matrix; Circulant matrix