A Direct Construction of Type-II $Z$ complementary code set with arbitrarily large codes

In this paper, we propose a construction of type-II $Z$-complementary code set (ZCCS), using a multi-variable function with Hamiltonian paths and disjoint vertices. For a type-I $(K,M,Z,N)$-ZCCS, $K$ is bounded by $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. However, the proposed type-II ZCCS provides $K = M(N-Z+1)$. The proposed type-II ZCCS provides a larger number of codes compared to that of type-I ZCCS. Further, the proposed construction can generate the Kernel of complete complementary code (CCC) as $(p,p,p)$-CCC, for any integral value of $p\ge2$.