A skew Hadamard matrix of order 36

Author:

Goethals J. M.,Seidel J. J.

Abstract

Hadamard matrices exist for infinitely many orders 4m, m ≧ 1, m integer, including all 4m < 100, cf. [3], [2]. They are conjectured to exist for all such orders. Skew Hadamard matrices have been constructed for all orders 4m < 100 except for 36, 52, 76, 92, cf. the table in [4]. Recently Szekeres [6] found skew Hadamard matrices of the order 2(pt +1)≡ 12 (mod 16), p prime, thus covering the case 76. In addition, Blatt and Szekeres [1] constructed one of order 52. The present note contains a skew Hadamard matrix of order 36 (and one of order 52), thus leaving 92 as the smallest open case.

Publisher

Cambridge University Press (CUP)

Reference7 articles.

1. Hadamard’s determinant theorem and the sum of four squares

2. Integral solutions to the incidence equation for finite projective plane cases of ordersn≡ 2 (mod4)

3. [1] Blatt D. and Szekeres G. , ‘A skew Hadamard matrix of order 52’, Canadian J. Math., to appear.

4. [5] Reid K. B. , and Parker E. T. , ‘Disproof of a conjecture of Erdös and Moser on tournaments’, J. Combinatorial Theory, to appear.

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