Hadamard matrices

A Hadamard matrix of order n is an n x n matrix of +1 and -1 whose rows (and therefore columns) are orthogonal. The famous Hadamard conjecture is that a least one Hadamard matrix exists for each order that is a multiple of 4.

In the following files there is one Hadamard matrix per line. The line consists of n hexadecimal numbers, one per row of the matrix. To obtain the actual rows, write the numbers in binary and change all zeros to -1.

Two Hadamard matrices are equivalent if one can be obtained from the other by permuting rows, permuting columns, and negating rows and columns.

The Hadamard matrices of order 32 were determined by Hadi Kharaghani and Behruz Tayfeh-Rezaie.

Equivalence classes of Hadamard matrices

order 4 (1)
order 8 (1)
order 12 (1)
order 16 (5)
order 20 (3)
order 24 (60)
order 28 (487)
order 32 (gzipped) (13710027)

For order 32, we also provide two further files. The first contains representatives of the extended equivalence classes when the transpose is regarded as equivalent to the original. The second contains representatives of the equivalence classes of matrices equivalent to their own transposes.

extended classes (gzipped) (6857010)
transpose-equivalent classes (gzipped) (3993)

 


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