A Construction of Arbitrarily Large Type-II $Z$ Complementary Code Set

Abstract

For a type-I $(K,M,Z,N)$-ZCCS, it follows $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. In this paper, we propose a construction of type-II $(p^{k+n},p^k,p^{n+r}-p^r+1,p^{n+r})$-$Z$ complementary code set (ZCCS) using an extended Boolean function, its properties of Hamiltonian paths and the concept of isolated vertices, where $p\ge 2$. However, the proposed type-II ZCCS provides $K = M(N-Z+1)$ codes, where as for type-I $(K,M,N,Z)$-ZCCS, it is $K \leq M \left\lfloor \frac{N}{Z}\right\rfloor$. Therefore, the proposed type-II ZCCS provides a larger number of codes compared to type-I ZCCS. Further, as a special case of the proposed construction, $(p^k,p^k,p^n)$-CCC can be generated, for any integral value of $p\ge2$ and $k\le n$.