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.
Hadamard matrices: skew of orders 276, 292 and symmetric 372
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
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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A database of constructions of Hadamard matrices
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.