A Direct Construction of Prime-Power-Length Zero-Correlation Zone Sequences for QS-CDMA System

In the recent years, zero-correlation zone (ZCZ) sequences have been studied broadly due to their significant application in quasi-synchronous code-division multiple access (QS-CDMA) systems. In this paper, we propose a direct construction of ZCZ sequences of prime-power-length using multivariable functions. In the proposed construction, we first propose a class of multivariable functions to generate a finite number of vectors having some specific properties which is further used to generate another class of multivariable functions to generate the desired ZCZ sequence sets. The proposed construction achieve the upper bound of $NZ\leq L$ asymptotically where $N,Z,$ and $L$ are number of sequences, ZCZ width, and length of sequence respectively. The constructed ZCZ sequence set is optimal for power of two length and asymptotically optimal for non power of two length. Additionally, we introduce a linear code that corresponds to the constructed ZCZ sequence set.