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

Iliya Bouyukliev 1 Veerle Fack 2, 3 Joost Winne 2, 3
1 IMI - Institute of Mathematics and Informatics [Sofia]
2 Department of Applied Mathematics and Computer Science [Ghent]
3 Ghent University - Research Group on Combinatorial Algorithms and Algorithmic Graph Theory
UGENT - Ghent University [Belgium]
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.
Keywords : Hadamard designs double-even self-dual codes
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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. ⟨hal-01184392⟩

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