  Z-complementary code set (ZCCS), an extension of perfect complementary codes
(CCs), refers to a set of two-dimensional matrices having zero correlation zone
properties. ZCCS can be used in various multi-channel systems to support, for
example, quasi-synchronous interference-free multicarrier code-division
multiple access communication and optimal channel estimation in multiple-input
multiple-output systems. Traditional constructions of ZCCS heavily rely on a
series of sequence operations which may not be feasible for rapid hardware
generation particularly for long ZCCSs. In this paper, we propose a direct
construction of ZCCS using second-order Reed-Muller codes with efficient
graphical representation. Our proposed construction, valid for any number of
isolated vertices present in the graph, is capable of generating optimal ZCCS
meeting the set size upper bound.
