Resumen
In this note we provide a counterexample which resolves conjectures about Hadamard matrices made in this journal. Beder [1998. Conjectures about Hadamard matrices. Journal of Statistical Planning and Inference 72, 7–14] conjectured that if H is a maximal m×n row-Hadamard matrix then m is a multiple of 4; and that if n is a power of 2 then every row-Hadamard matrix can be extended to a Hadamard matrix. Using binary integer programming we obtain a maximal 13×32 row-Hadamard matrix, which disproves both conjectures. Additionally for n being a multiple of 4 up to 64, we tabulate values of m for which we have found a maximal row-Hadamard matrix. Based on the tabulated results we conjecture that a m×n row-Hadamard matrix with mgreater-or-equal, slantedn-7 can be extended to a Hadamard matrix.