On optimal construction of two classes of ZCZ codes

This paper presents constructions of two kinds of sets of sequences with a zero correlation zone, called ZCZ code, which can reach the upper bound of the member size of the sequence set. One is a ZCZ code which can be constructed by a unitary matrix and a perfect sequence. Especially, a ternary perfect sequences with elements I and zero can be used to construct the proposed ZCZ code. The other is a ZCZ code of pairs of ternary sequences and binary sequences which can be constructed by an orthogonal matrix that includes a Hadamard matrix and an orthogonal sequence pair. As a special case, an orthogonal sequence pair, which consists of a ternary sequence and a binary sequence, can be used to construct the proposed ZCZ code. These codes can provide CDMA systems without co-channel interference.