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arXiv · 1503.04226

Symmetric Hadamard matrices of order 116 and 172 exist

Olivia Di Matteo·Dragomir Z. Djokovic·Ilias S. Kotsireas
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Abstract

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 construction is based on a recent new combinatorial array discovered by N. A. Balonin and J. Seberry. For order $116$ we used an adaptation of an algorithm for parallel collision search. The adaptation pertains to the modification of some aspects of the algorithm to make it suitable to solve a 3-way matching problem. We also point out that a new infinite series of symmetric Hadamard matrices arises by plugging into the GP array the matrices constructed by Xia, Xia, Seberry, and Wu in 2005.

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Olivia Di Matteo, Dragomir Z. Djokovic, Ilias S. Kotsireas. 2015-03-13. Symmetric Hadamard matrices of order 116 and 172 exist. https://doi.org/10.1515/spma-2015-0022

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