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Let A be an m × n, (0, 1)-matrix. A submatrix of A is odd if the sum of its entries is an odd integer and even otherwise. The maximum number of 2×2 odd submatrices in a (0, 1)-matrix is related to the existence of Hadamard matrices and bounds on Turán numbers. Pinelis [On the minimal number of even submatrices of 0-1 matrices, Designs, Codes and(More)
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