Complex Hadamard Matrices and Strongly Regular Graphs
Combinatorics
2020-11-04 v2
Abstract
Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph contains a Hadamard matrix then is either of Latin square type or of negative Latin square type. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency algebras. Moreover we show that there are only three distance regular covers of the complete graph that give complex Hadamard matrices.
Keywords
Cite
@article{arxiv.1102.5601,
title = {Complex Hadamard Matrices and Strongly Regular Graphs},
author = {Ada Chan},
journal= {arXiv preprint arXiv:1102.5601},
year = {2020}
}