A New Construction Method of Gray Maps for Groups and its Application to the Groups of Order 16

In this paper we propose a new construction method of Gray maps for groups. In a earlier paper, we succeeded the Type 1 construction for all groups of order 16 and confirmed that we can construct Type 2 maps for several groups of order 16, but failed to construct such maps for other groups. Therefore, in this paper we try to apply the new construction method to them.