2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order,and their related Hadamard matrices and codes |
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| Authors: | Iliya Bouyukliev Veerle Fack Joost Winne |
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| Institution: | (1) Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, P.O. Box 323, 5000 Veliko Tarnovo, Bulgaria;(2) Research Group on Combinatorial Algorithms and Algorithmic Graph Theory, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281–S9, 9000 Ghent, Belgium |
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| Abstract: | We present the full classification of Hadamard 2-(31,15,7), Hadamard 2-(35, 17,8) and Menon 2-(36,15,6) designs with automorphisms
of odd prime order. We also give partial classifications of such designs with automorphisms of order 2. These classifications
lead to related Hadamard matrices and self-dual codes. We found 76166 Hadamard matrices of order 32 and 38332 Hadamard matrices
of order 36, arising from the classified designs. Remarkably, all constructed Hadamard matrices of order 36 are Hadamard equivalent
to a regular Hadamard matrix. From our constructed designs, we obtained 37352 doubly-even 72,36,12] codes, which are the
best known self-dual codes of this length until now.
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| Keywords: | Hadamard design Hadamard matrix Self-dual codes |
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