Small orders of Hadamard matrices and base sequences

Dragomir Z. Djokovic

Small orders of Hadamard matrices and base sequences

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arxiv 1008.2043 v1 pith:CI5TO2OV submitted 2010-08-12 math.CO

Dragomir Z. Djokovic This is my paper · ORCID

classification math.CO

keywords baseexistfirsthadamardlengthsequencescaseconsequently

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We update the list of odd integers n<10000 for which an Hadamard matrix of order 4n is known to exist. We also exhibit the first example of base sequences BS(40,39). Consequently, there exist T-sequences TS(n) of length n=79. The first undecided case has the length n=97.

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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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