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In this paper we consider Type 1 Gray maps and Type 2 Gray maps for groups oforder 16. First, we confirm that we can construct Type 1 Gray maps for allgroups of order 16, and we actually construct them. Next, we confirm that wecan construct Type 2 Gray maps for several groups of order 16, and we constructall such maps. Finally we reveal why the other groups do not admit Gray maps.

Construction of Gray maps for groups of order 16