Group symmetries of complementary code matrices

Complementary code matrices (CCMs) generalize Golay pairs and Hadamard matrices. In this paper, we describe new group relations satisfied by CCM-preserving symmetries and use its symmetry group to classify CCMs in terms of their equivalence classes. We also give an upper bound on the order of this group, determine the number of equivalence classes of N × 4 quad-phase CCMs where N = 2, 3, 4, 5, 6, and present a new construction to generate quad-phase CCMs from ternary CCM dual pairs.