On Skew E-W Matrices

An E–W matrix M is a ( − 1, 1)‐matrix of order 4t+2, where t is a positive integer, satisfying that the absolute value of its determinant attains Ehlich–Wojtas' bound. M is said to be of skew type (or simply skew) if M−I is skew‐symmetric where I is the identity matrix. In this paper, we draw a parallel between skew E–W matrices and skew Hadamard matrices concerning a question about the maximal determinant. As a consequence, a problem posted on Cameron's website [7] has been partially solved. Finally, codes constructed from skew E–W matrices are presented. A necessary and sufficient condition for these codes to be self‐dual is given, and examples are provided for lengths up to 52.