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Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes

Abstract : Before this work, at least 762 inequivalent Hadamard matrices of order 36 were known. We found 7238 Hadamard matrices of order 36 and 522 inequivalent [72,36,12] double-even self-dual codes which are obtained from all 2-(35,17,8) designs with an automorphism of order 3 and 2 fixed points and blocks.
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Iliya Bouyukliev, Veerle Fack, Joost Winne. Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.93-98, ⟨10.46298/dmtcs.3435⟩. ⟨hal-01184392⟩

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