44×44 {-1, +1} matrices of maximal determinant

|Det Rj| = 162805498773679522226642×243 = 22×1121×243

Ratio of |Det Rj| to Hadamard bound: 1

M=RjTRj= Rj RjT=44 I
where I is the 44×44 identity matrix.


  1. Maximal matrix first reported by Paley [P].
  2. Svetlana Topalova has classified the Hadamard matrices of order 44 with automorphisms of order 7 and found their number to be 384 [To]. They are available from her web page.
  3. Christos Koukouvinos has files of 6018 Hadamard matrices and 784 skew-Hadamard matrices on his home page. Jennifer Seberry's web site lists a Williamson-type Hadamard matrix of order 44.

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Page created 26 January 2002.
Last modified 31 October 2004.
Comments: maxdet@indiana.edu