Classiﬁcation of Hadamard matrices of small orders Behruz Tayfeh-Rezaie Second SBU Combinatorics Day Second SBU Combinatorics Day Shahid Beheshti University, May 11, 2016 Honoring 50th anniversary of Behzad’s Conjecture A ll equivalence classes of Hadamard matrices of order at most 28 had been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. In 2014, using an exhaustive computer search we showed that there are exactly 13,710,027 Hadamard matrices of order 32. The next open case is order 36. Recently, we have tried to classify some types of Hadamard matrices of order 36. In this talk we present our approach and also report some partial results on the classiﬁcation in order 36. 1

Second SBU Combinatorics Daycombinatorics.sbu.ac.ir/DrTayefeh.pdfSecond SBU Combinatorics Day Second SBU Combinatorics Day Shahid Beheshti University, May 11, 2016 Honoring 50th anniversary

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Page 1: Second SBU Combinatorics Daycombinatorics.sbu.ac.ir/DrTayefeh.pdfSecond SBU Combinatorics Day Second SBU Combinatorics Day Shahid Beheshti University, May 11, 2016 Honoring 50th anniversary

Classification of Hadamard matrices of smallorders

Behruz Tayfeh-Rezaie

Second SBU Combinatorics DaySecond SBU Combinatorics DayShahid Beheshti University, May 11, 2016Honoring 50th anniversary of Behzad’s Conjecture

All equivalence classes of Hadamard matrices of order at most 28 hadbeen found by 1994. Order 32 is where a combinatorial explosionoccurs on the number of Hadamard matrices. In 2014, using an

exhaustive computer search we showed that there are exactly 13,710,027Hadamard matrices of order 32. The next open case is order 36. Recently,we have tried to classify some types of Hadamard matrices of order 36. Inthis talk we present our approach and also report some partial results on theclassification in order 36.