Construction of Regular Hadamard Matrices From Circulant Hadamard Matrices and Ryser’s Conjecture

Pankaj Kumar Manjhi; Jitendra Kumar

doi:10.26713/cma.v16i3.3215

Authors

Pankaj Kumar Manjhi University Department of Mathematics, Vinoba Bhave University, Hazaribag, Jharkhand, India https://orcid.org/0000-0001-9196-3002
Jitendra Kumar University Department of Mathematics, Vinoba Bhave University, Hazaribag, Jharkhand, India https://orcid.org/0009-0005-0132-7755 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v16i3.3215

Keywords:

Hadamard matrix, Partial Hadamard matrix, Circulant matrix

Abstract

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.

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