:Given an Hadamard matrix of order 4 " a " in standardized form, remove the first row and first column and convert every " 1 to a 0.
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This construction is reversible, and the incidence matrix of a symmetric 2-design with these parameters can be used to form an Hadamard matrix of size 4 " a ".
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This construction is reversible, and the incidence matrix of a symmetric 2-design with these parameters can be used to form an Hadamard matrix of order 4 " a ".
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An Hadamard matrix can be put into " standardized form " ( that is, converted to an equivalent Hadamard matrix ) where the first row and first column entries are all + 1.
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An Hadamard matrix can be put into " standardized form " ( that is, converted to an equivalent Hadamard matrix ) where the first row and first column entries are all + 1.
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Now, we need to show that the matrix \ mathit { E _ c } whose rows are the nonzero codewords, constitutes a cyclic core for some complex Hadamard matrix \ mathit { H }.
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It is a 2 & times; 2 Hadamard matrix, and its rows form the basis of a diagonal square lattice consisting of the integer points whose coordinates both have the same body-centered cubic lattice.
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*PM : proof that Hadamard matrix has order 1 or 2 or 4n, id = 9095 new !-- WP guess : proof that Hadamard matrix has order 1 or 2 or 4n-- Status:
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*PM : proof that Hadamard matrix has order 1 or 2 or 4n, id = 9095 new !-- WP guess : proof that Hadamard matrix has order 1 or 2 or 4n-- Status:
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Reid and Brown in 1972 showed that there exists a " doubly regular tournament of order " n " " if and only if there exists a skew Hadamard matrix of order " n " + 1.
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