• Number of equivalent Hadamard matrices

    From budishin@gmail.com@21:1/5 to All on Sun Aug 14 06:14:27 2016
    Hadamard matrices exist for most sizes that are multiples of 4. A great
    deal of research was done to find for which matrix size these Hadamard
    matrices exist and to determine the number of non-equivalent Hadamard
    matrices. To cite Wikipedia: "Two Hadamard matrices are considered
    equivalent if one can be obtained from the other by negating rows or
    columns, or by interchanging rows or columns. Up to equivalence, there
    is a unique Hadamard matrix of orders 1, 2, 4, 8, and 12. There are 5 inequivalent matrices of order 16, 3 of order 20, 60 of order 24, and
    487 of order 28. Millions of inequivalent matrices are known for orders
    32, 36, and 40."

    However what I am interested in is to find how many equivalent matrices
    exist for a given inequivalent matrix. The maximum number of equivalent matrices for matrix size M x M would be:

    2^M x 2^M x M! x M!

    However if you make all sign changes and row and column permutations
    you end up with many of repetition. I am looking for some research
    which would determine the number of unique equivalent matrices. Or
    which would identify the source of repetitions.

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