  An $n$ by $n$ skew-symmetric type $(-1,1)$-matrix $K=[k_{i,j}]$ has $1$'s on
the main diagonal and $\pm 1$'s elsewhere with $k_{i,j}=-k_{j,i}$. The largest
possible determinant of such a matrix $K$ is an interesting problem. The
literature is extensive for $n\equiv 0 \mod 4$ (skew-Hadamard matrices), but
for $n\equiv 2\mod 4$ there are few results known for this question. In this
paper we approach this problem constructing cocyclic matrices over the dihedral
group of $2t$ elements, for $t$ odd, which are equivalent to $(-1,1)$-matrices
of skew type. Some explicit calculations have been done up to $t=11$. To our
knowledge, the upper bounds on the maximal determinant in orders 18 and 22 have
been improved.
