Complex Hadamard Matrices and Strongly Regular Graphs

Details Complex Hadamard Matrices and Strongly Regular Graphs Complex Hadamard Matrices and Strongly Regular Graphs

2011-02-28

arxiv.org/abs/1102.5601v1

Mathematics

Combinatorics

Scientific paper

Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph $X$ contains a Hadamard matrix then $X$ 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.

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