Combinatorial properties of Circulant Hadamard matrices
Luis H. Gallardo, Olivier Rahavandrainy, Reinhardt.Euler
TL;DR
This paper investigates the combinatorial characteristics of circulant Hadamard matrices, using their orthogonality properties to identify and exclude certain matrix configurations, advancing understanding of their structure.
Contribution
It introduces new combinatorial constraints on circulant Hadamard matrices, helping to eliminate specific forms and deepen structural insights.
Findings
Certain forms of circulant Hadamard matrices are shown to be impossible.
Orthogonality conditions lead to new combinatorial exclusions.
The results refine the classification of these matrices.
Abstract
We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.
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Taxonomy
Topicsgraph theory and CDMA systems · Mathematics and Applications · Advanced Scientific Research Methods