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We construct Hadamard matrices of orders    4  ·  251  =  1  ,    004    and    4  ·  631  =  2  ,    524   , and skew‐Hadamard matrices of orders    4  ·  213  =  852    and    4  ·  631  =  2  ,    524   . As far as we know, such matrices have not been constructed previously. The constructions use the Goethals–Seidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.

Some New Orders of Hadamard and Skew‐Hadamard Matrices