Skew-Hadamard matrices of orders 188 and 388 exist

Dragomir Z. Djokovic

Skew-Hadamard matrices of orders 188 and 388 exist

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arxiv 0704.0640 v2 pith:O5X4EPIO submitted 2007-04-04 math.CO

Dragomir Z. Djokovic This is my paper · ORCID

classification math.CO

keywords matricesordersconstructconstructeddifferencefamiliesskew-hadamardarray

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We construct several difference families on cyclic groups of orders 47 and 97, and use them to construct skew-Hadamard matrices of orders 188 and 388. Such difference families and matrices are constructed here for the first time. The matrices are constructed by using the Goethals-Seidel array.

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A database of constructions of Hadamard matrices
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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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