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Hadamard matrices: skew of orders 276, 292 and symmetric 372

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arxiv 2301.02751 v3 pith:HY7J27LA submitted 2023-01-07 math.CO

Dragomir Ž. Djoković This is my paper · ORCID
classification math.CO
keywords matricesorderconstructfirsthadamardmatrixskew-hadamardsymmetric
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The smallest integer v>0 for which no skew-Hadamard matrix of order 4v is known is v=69. We show how to construct several such matrices. We also construct presumably the first example of a skew-Hadamard matrix of order 292, and the first examples of symmetric Hadamard matrices of order 372.

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  1. A database of constructions of Hadamard matrices

    math.CO 2024-11 conditional novelty 6.0 of 10

    A verified SageMath database now constructs all known Hadamard matrices up to order 1208, corrects the skew Hadamard order 292, updates over 100 table entries, and proves Paley constructions fail for order 2^m times 509203.

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