On (-1,1)-Matrices of Skew Type with the Maximal Determinant and Tournaments

Skew Hadamard matrices of order n give the solution to the question of finding the largest possible n by n determinant with entries +/- 1 of skew type when n equivalent to 0 (mod 4). Characterizations of skew Hadamard matrices in terms of tournaments are well-known. For n equivalent to 2 (mod 4), we give a characterization of (-1, 1)-matrices of skew type of order n where their determinants reach Ehlich-Wojtas' bound in terms of tournaments.