Symmetric Hadamard matrices of order 116 and 172 exist

Olivia Di Matteo, Dragomir Z. Djokovic, Ilias S. Kotsireas

We construct new symmetric Hadamard matrices of orders $92,116$, and $172$. While the existence of those of order $92$ was known since 1978, the orders $116$ and $172$ are new. Our…