New supersets of Zadoff-Chu sequences via the Weil bound

Sequences with low correlation have important applications in communications, radar, and cryptography. Recently, Pitaval et al. proposed two enlarged supersets of Zadoff-Chu (ZC) sequences with low correlation zone (LCZ) property to overcome physical random access channel (PRACH) capacity shortfall in 5G. In this paper, we present several classes of generalized supersets of ZC sequences using the Weil bound of exponential sums over finite fields. We employ ZC sequences and traditional sequences like m-sequences, binary Gold sequences and p-phase sequences as covers to propose several new classes of supersets of ZC sequences. The proposed sequence families have more flexible parameters compared to previous constructions. Interestingly, one of the resultant sequence sets is asymptotically optimal with respect to the Welch bound.