Conjectures Made by Me and Others (Please indicate your claims))

  • The first unresolved case is order 32 for which I suspect there are over 33,000 Inequivalent Hadamard Matrices.

  • There are certainly hundreds and probably thousands of Inequivalent Hadamard matrices for orders 36, 44, 52, .....

  • I conjecture that as the power of two increases (eg 32 is 2^5 while 36 is 2^2x9) the number of inequivalent cases increases dramatically.

  • I conjecture that the number of Inequivalent Hadamard Matrices of order 36 which are regular (ie have constant row and column sum) is over 100. I conjecture that there are tens of Reqular Inequivalent Hadamard Matrices of order 36 which are not equivalent to a symmetric Reqular Hadamard Matrices of order 36.

    Matrices of Order 16

    Marshall Hall's five inequivalent matrices (16H1 , 16H2 , 16H3 , 16H4 , 16H5 )

    Some Constructions for order 20

    Three inequivalent matrices (20H01 , 20H02 , 20H03 ). The first is Paley I Construction, the second and third are Tonchev iii and 1v.

    Noburo Ito's 60 inequivalent matrices of order 24

    see "Neil Sloane 's Library List". Profiles of inequivalent matrices. Defining sets for inequivalent matrices.

    Kimura's 487 inequivalent matrices of order 28

    see "Neil Sloane 's Library List"

    For GECP for some of Kimura's Hadamard matrices Gaussian Elimination with Complete Pivoting.

    Some Constructions for order 32

    Sylvester Construction (32Syl ), Paley I Construction (32P02 ), Paley II Construction (P12, P13, P14, P15, P16, P17, P18, P19), Marshall Hall Difference Set Construction (32H03 ), W D Wallis Inequivalent (Code 32G05, 32G06, 32G07, 32G08, 32G09, 32G10, 32G11, 32G12, 32G13, 32G14, 32G15).

    Also refer to "Neil Sloane's Library List"

    An Extended Library of Hadamard Matrices

    32Syl 32P02 32H03 32G05 32G06 32G07 32G08 32G09 32G10 32G11 32G12 32G13 32G14 32G15 P12 P13 P14 P15 P16 P17 P18 P19

    Some Constructions for order 36

    Eleven matrices found by Vladimir Tonchev
    36H140 , 36H141 , 36H142 , 36H143 , 36H144 , 36H145 , 36H146 , 36H147 , 36H148 , 36H149 , 36H150 ).

    179 Further Hadamard matrices of order 36

    Bush-type Hadamard matrix of order 36 found by Zvonimir Janko

    Regular Hadamard matrices of order 36 found by Jennifer Seberry

    Updated 6th June, 2001. Please email questions or comments to