  In this paper, we study trigonal minimal surfaces in flat tori. First, we
show a topological obstruction similar to that of hyperelliptic minimal
surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat
torus must be 1 (mod 3). Next, we construct an explicit example in the higher
codimensional case. This surface satisfies good properties and is theoretically
distinct from traditional examples.
